From experience I would not take a down bag out without a cover, or bivvy bag. I used to cycle bivvy up in the lakes with a collie dog, my first bivvy bag was a £100 goretex jobby from Survival Aids of Penrith. I am after one now, but my place of looking is ebay, for ex military gore tex bags, they on there go for about £35 maximum and sometimes a hell of a lot cheaper. If you search on there type in variations on the name bivi as ex pongos can't spell.
The experience of unprotected down, well, in my tent which was/is a Saunders Spacepacker plus which I sometimes used with flysheet only for cycle camping( could take the bike inside and have plenty of room for oneself and the dog), I dropped a cup of coffee on the sleeping bag, it was buggered for days and stained on the inside, to look as if one had had an accident in there.
Quite simple down gets wet, it is next to useless for thermal insulation, have down, get gore tex bivi bag and as soon as the sleeping bag comes out bung it it is the goretex as the first job you do even if you are not using it for a while, as loosing something like that in winter is not a good survival move and minus whatever in ice and snow can be survival.
But if snow is deep enough, try digging a snow hole, they are fun and surprisingly comfortable. Having a dog with you is like having a portable heater.