In reply to benp1:
Bear in mind that wind blown snow is much much worse at dog height than your head height and make allowance. IE you might be doing OK but need to turn back for the dog's sake.
I had my collie on a multi day ski tour some years ago and had to de-ice her eye / face a number of times using my breath/lips to melt the ice: couldn't just pull it off!
If overnighting be prepared to share your pit, it is only fair
Dogs often try and help you dig snow holes but aren't really much help...they just go down so far, then curl up in their little hole whilst you slave for a couple of hours making a palace for them. Seems fair enough I guess
Other folk have mentioned a bothy bag....essential kit. If camping make sure your tent has minimal wind flap. My dog suffered very much one night with the noise driving her demented [literally; crazed look, eyes 'gone',] had to bail out in the dark/blizzard, and she wouldn't camp again for years.
Dogs claws work very well up hill, they are unlikely to have issues unless really icy. However, down hill is a different matter. Mine liked to tuck right behind my legs on the steep downs. Not good as she threatened to knock me over, or I was in danger of putting a crampon through her paws. [carry a dog first aid kit].
Think very carefully about stream crossings. As an inexperienced pup she once threw herself into a river, not fancying the swinging, rickity bridge. She was swept downstream a bit but got across. Obviously soaking wet: not good in the middle of winter and a snow hole night ahead! We both learned from that one. Plan for bridges on your route and put dog on lead in good time. Especially labs who love water ! Now is not the time.
Train dog to be carried draped over your shoulders.....stream crossings where you need to carry the dog, deer fences to cross etc, and if injured [dump the contents of your sack, 'cept what you both need to get off the hill]. Dogs love to play in the snow but recognise when this isn't a good thing and bring dog to heel / be calm.
Dog needs to ignore livestock and especially deer and mountain hares. I have known dogs disappear for hours after deer. Some never come back, or are lost for weeks. If you loose contact in poor weather etc you have to rely on the dog finding you, which if the wind is wrong they may not be able to do. Prior training essential!
It is very rewarding going off in winter with your hound, but it puts a lot of responsibility on you, perhaps literally on your shoulders....