Winter backpacking with a dog

Try car camping with your dog first. If you need snowshoes or skis they will wear themselves out in fresh snow, transitional snow is best. You need to protect domestic dog's paws with booties. They need water a badly as you do and if you have to wear sunglasses they are struggling too.

Why car camping first? I've camped with my dog before just not in winter, and since we live in Tahoe I snowshoe and ski with her on a daily basis. When it is really deep, she just follows my tracks.

As far as booties–she absolutely hates them. I trim the hair between her paw pads to resist balling and she doesn't seem to have problems. I also put a sort of balm that I got at the local pet store on her pads as it resists snow and cold well (at least I think…). I plan on bringing booties with me to put on her if she shows signs of discomfort, but she never has so far.

I have a synthetic vest that fits her well, and I'm thinking an old fleece sleeping bag would be good for her when it is quite cold. For shelter I'm considering getting a new 4-season tent (Hilleberg Nallo 3) as I currently have a 2-person Bibler Eldorado w/o a vestibule that isn't big enough.

Anyone else have experience winter backpacking with dogs? Insulation? Shelter type and size?

Good housekeeping will go a long way with a dog in a tent, different temps, snow conditions, and type of fur lead to possible mess. I tried to keep mine in the vestibule but he finally pesuades me to come all the way in. Car camping is just a way test run everything with an escape clause, doesn't sound like anything you need.
The booties came from seeing the blood trail off his paws after crossing a hillside of breakable crust. He had been skijornig for two months and still cut up his paws.
Good Luck.