Your dog is an adult, is “in” coat (hasn’t recently blown every hair on his/her body), you keep your dog dry and out of the wind for sleeping, and you feed well, it’ll be fine in winter temperatures.
I don’t know the exact coldest temp that I’ve tent camped with a dog, but it was well below zero degrees F. Probably -10, -15.
Insulation from the frozen ground is key, same as for us. I usually start with a reflective space blanket flipped shiny side up on my tent floor, then put my underlayments on that. Since they’re lightweight and can fit anywhere, bring an extra, as dog claws can shred them accidentally.
If your dog is COMPLETELY dry, you can use your own spare clothes for dog “nesting”, if your dog is inclined, and you need to keep weight down. Snuggling is great if your dog is a snuggler (one of mine is, the other is not) but aim their face away from your face so you don’t get all the condensation, frost, and water around your own head.
Watch for ice balls that form in their paw pads, make sure you pick those out before you let them into the tent. They melt into an unholy volume of water....
Feed good rich fat-containing food at night before bed, it keeps them warm while they sleep. And make sure they’re hydrated. I’ve cut either chunks of butter or fed sardine packets with the evening meals when it’s very cold. And lots of extra food, close to double the usual amount. My winter backpacking buddy has always owned huskies, and she got me started on the “fat before bed” dog feeding.
The famed “Costco quilts” (read about them on winter hammock forums if you’re curious) are excellent as a throw-over dog cover for bitter cold. They are down, super light weight, packable, and inexpensive enough that you won’t cry if something bad happens to one.
I used to do this quite often, but it’s been a few years (work gets in the way, alas). Beautiful photos, enjoy your travels!