I've just been getting our kit ready and I thought I'd share my thoughts on winter gear. To start here is our kit all laid out (minus first aid kit which I'm still sorting out)
This is Emma's (just turned 9) kit. If Emma is coming winter hiking it will tend to be lower level hills, I wouldn't take her anywhere requiring ice axe/crampons. She has microspikes which are really useful for frozen ground and paths. I've found these adequate for the conditions we've had this winter where we are and where we tend to walk.
Emma like me suffers from cold hands so she has three pairs of gloves in her bag. She has a thin pair of sprayway gloves which sit nicely under her mittens. They were fairly pricey and came as a Christmas present, you can probably get cheaper versions in somewhere like Trespass or mountain warehouse. The best buy were the pink waterproof mittens - they came from Mountain Warehouse which people have been quite derogatory about but these mitts have been really good, they've kept my daughter's hands nice and snug in the rain and snow and they is plenty of room for a second pair of gloves underneath. As a top layer I prefer mittens as trying to put a pair of gloves on top of a pair of gloves is not easy, having mittens allows for the top layer to easily be taken off for a lunch stop or when more dextaritory is required. She also carries a spare pair of insulation woolen mittens. Loads of places sell cheap kids gloves - wooley gloves can be found for cheap on Ebay or for ski gloves keep and eye out in Lidl and Aldi.
She also carries a buff, hat, fleece buff & balaclava. For both me and Emma getting balaclavas were our BEST purchase ever. I don't care what I look like in one, they are so cosey when the wind is howling around and sit so much nicer under a hood than a had does (although when it is really cold I add a hat on top too!) Most your heat is lost through your head so keeping it warm is essential. I sometimes stick my balaclava on during lunch stops to hold my body heat in. Who cares what you look like on the hill, it is not a fashion parade and your probably not likely to say anyone else up there anyway! The buff can be used as a hat when it is hot and is ridiculously light, it too can be made into an improv balaclava. Ebay is full of cheaper versions.
We both carry Petzl torches- Tikkina2 - I can't rate Petzl enough I have seriously abused my other Petzl torch when caving and it keeps on going. There battery life is excellent. I've used it on many occasions on winter walks. I've only even used it on fairly easy terrain though, I think if I was tackling more rocky/scrambly conditions I'd go for a Petzl Myo which is extremely bright. Head torches can be picked up for as little as £4, just make sure you test it before you need it to make sure it is bright enough for your needs!
We always have waterproofs even if no rain is forecast (I am probably over cautious in this sense, but having been caught out on a coastal walk in forecast by a torrential downpour 3 miles from our accommodation I do now always take them - we were shivering by the time we arrived back and our boots were full of water) For waterproof trousers we both have Berghaus - for me given the level of walking we do it's not something I'd scrimp on. When we first started walking I got the cheapy Regatta ones which are fine for a walk in a woods but if your spending a whole day in the rain you will be soon soaked through, and they tend to rip very easily. I also tried Sprayway, but their zips did not go high enough and they could not be pulled on over Emma's boots which is no good if your in a hurry - no-one wants to be taking their boots off in the rain! You can often get these by finding the cheapest price online and taking it to Go Outdoors to get them to price match. If you have a Go Outdoors card (which can be purchased in store) they will price match and take off 10%. In respect of waterproof coats we both wear Sprayway - which is more of a budget line but I've found them to be good as long as they are reproofed at intervals (you can buy reproofing spray at most outdoor shops).
From November until present date (March) we have been wearing thermals under our clothes for walking. If you have no thermals at least make sure you layer up - when I first started walking I'd wear leggings or tights under my trousers and would take a few extra fleeces. Aldi and Lidl often sell thermals during the winter and I've picked up spare ones in Premark too. For winter I wear my winter lined trousers which I got in Lidl about 3 years ago, despite lots of abuse and repair they are still going strong. I recently treated myself to a merino wool thermal top from Trespass in the sale, it was around £20 which felt expensive at the time but it has been excellent, despite getting hot and bothered going up hill it's still felt comfy and sweat free. I used my Christmas money to purchase it so it didn't feel like a huge expense!
Also with Christmas money we bought ourselves a down jacket each, this was to go in our bag as an extra layer for emergencies or to wear when it's really cold. Down is really lightweight so you hardly notice it is there, it is also really warm too. Emma's is a Karrimor one which came from Sports Direct for around £20. They have been useful for lunch stops when you often need an extra layer to keep the chill off when you cool down.
We use dry bags which also came from Sports Direct as a gift, but for those on a budget a black sack or plastic bags do just fine. I use mine to keep my hat/gloves etc separate from everything else so I can get them out quickly when in a hurry.
I carry a big orange survival bag and we both have a whistle on our packs. I read a book recently which contained a tale about a child getting separated from their parent on a mountain so also purchased my daughter a whistle as I'd assumed one was enough before. We also carry OS map/Compass/basic GPS. My GPS is garmin and is good for getting a grid reference from if you are stuck. It doesn't display maps though.
A year or so back I purchased a survival shelter (also known as bothy shelter) They look like the picture below, but cram down really small into a stuff sack. Mine weighs about the same weight as my survival bag, you pull if over your heads and sit on the edges. It's like a single skin tent without poles. When it is cold/wet/windy these are great for lunch stops, in an accident I imagine one of these would be worth it's weight in cold to keep off the elements. My daughter begs to get it out even when it's not raining as she loves the novelty of a lunch stop in a 'tent'!
My daughter received a thermal mug from Father Christmas which has been good for carrying hot squash. She also has one of my walking poles which has lost a section. As she is only small it is the right size for her. I also carry walking poles - I know people are often cynical about them for young people, but I've found them really useful. They really help for going uphill and are especially useful in slippery conditions for keeping you upright. I don't use the hand straps as I worry I'd break my wrist if I could not release my hand if I fell
For boots I have struggled to find good heavy duty boots for my daughter, we do so much walking most kids boots will get trashed. The Hi-tech ones we tried had no removable insole so after many a wet walk despite being dried out the inner sole simply rotted! The last pair my daughter had was Brasher Tora - these can be purchased in Field and Trek/Go outdoors etc. The uppers don't last long as the stitching eventually degrades but in terms of the ankle support and tread on the boot they seem to be the best of a bad bunch!
Above is the contents of my bag. Also pictured are my gaiters - Emma also has a pair. When I first started walking I always associated them with rambling type groups, but after a few boggy walks it wasn't long before I bought a pair for me and Emma. With Emma being so small on boggy ground water can often reach the top of her boot - the gaiters have been excellent in keeping her feet dry in those kind of conditions.
My axe has made it into the picture - as I will be walking with my daughter this holiday we won't be doing any mountains, but I may take the chance to practice some winter skills if I can find a decent slope.
In terms of drinking we tend to use hydration bladders - easier for a kid to drink from one of those than to stop when it's cold and faff with a bottle. If your in conditions below freezing I find it keeps it unfrozen if you blow back down the tube every now and again. When it does freeze I find if I stick the tube down my top my body heat is enough to unfreeze it in a few minutes.
Bag wise Emma has a Vaude kids rucksack - again as she only has a tiny frame I needed to find a bag small enough and light enough to suit her. I have two bags, the smaller one in the picture and a bigger one for if I'm carrying axe/crampons
Emma and I learnt to hike together and learnt to stay safe in the mountains together. She has carried her own gear since 4 years old without complaint and we love exploring the mountains, woods, hills countryside together. I think people think I sometimes overkill it in terms of what we take, but when walking even at low level in the winter I want to keep my most special person safe.
Lastly I am a bit of a planning obsessive. A really excellent website I use for mapping walks is Walk Highlands. It allows me to plot my route (for anywhere in the country) and will tell me how long a route will take (minus lunch/camera/faff stops) and how far/how much ascent there is. It has been invaluable at times.
For those who know me I am also obsessed with the weather! Before embarking on a trip I tend to check Met Office mountain forecast. They also now do a summit forecast. Mountain Weather Information Service is useful too
Local webcams also provide good information - I have only link a few as examples but a simple google will find more
I am also Facebook friends with the mountain rescue teams in the areas I walk in - their updates regarding weather conditions on the hill are often the more comprehensive and tell what is actually like out there, as opposed to the forecast which will tell you what it going to be like.