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?