Having been quoted as an "expert" above I feel obliged to respond. Actually, I don't backpack in winter, mostly because I can't stand 14-15 hour nights in the tent. Once it's pitch dark more than 12 hours a day, it's just dayhiking for me, and usually below the snowline.
However, I do backpack in "shoulder season" which in the high Cascades can mean temps down to 15*F. I take a Gossamer Gear torso length Nightlite pad for my dog (it helps support my pack, since I use an insulated air pad), and if below freezing temps are expected, I'll put a dog jacket in my dog's pack. Hysson is mostly Lab, and of course has that very fine, dense (and perpetually shedding!) undercoat designed to let him survive in freezing water, but since he's an indoor dog at home, he doesn't have as much as if he were outdoors most of the time. It's really important to have a dog jacket loose enough that it doesn't compress the dog's natural furry insulation!
Because Hysson stands up and stretches every few hours during the night and then turns around three times before lying back down (I call him my Robert Benchley dog), I've found it's useless to put a blanket or other cover on him. It will end up in a back corner of the tent. That's why I use a jacket to keep him warm on cold nights. On cold nights he is definitely part of my sleep system!
Should I ever want to camp in zero F temps, my daughter recently gave me a really heavy fleece coat she had for her Viszla (their hair is so short and thin that they need a lot of covering--in fact, she used it under a rain jacket). It's "Apache River" brand and has more belly coverage than most fleece dog coats. However, those who sew can probably convert a thrift shop child's fleece jacket for their dog for a lot less money.
Actually, Hysson's biggest snow experience was last week in Seattle, of all places. It started snowing Tuesday morning and, except for a few bouts of freezing rain, never really stopped until warmer rains hit on Saturday. Awesome sledding on the steep hills near my son's place. Most of the parents were out, too, making sure their kids didn't slide into the few cars that were trying to venture out. My grandkids had a ball, and so did their parents. My son said that the rare snowstorms are really the only time that the neighborhood gets together as a community! We were out for several hours each day. Hysson was just fine in the snow, although his paws got a bit sensitive, especially later in the week when the snow had a nice crust on top from the freezing rain.