Honestly, in the winter with temps in the 20s and lower, my flat strategy is to push the bike. I dress lightly so I don't get too warm when I ride, but the flip side is if I'm not moving I'm not generating heat and could quickly become hypothermic. Pushing the bike at least keeps me moving. Also, taking off my gloves to try and fix a flat in those temps would be really low on the fun scale.
I'll fix a flat on the road during warmer temps, but all of those bikes have tubes in them.
So far I've been lucky that most of my fat flats have been within a couple of miles of the office or home. I did have one flat on the fat bike about 3.5 miles from the office, while there was heavy unplowed snow. I carried the fat bike for about a mile and a half and must have looked pathetic enough that a guy in a truck stopped and gave me and the bike a ride the rest of the way to the office.
I just went down to the garage and pumped up my tire and it seems to be holding air just fine now. I suppose sitting in the heated parking area all day the sealant thawed out enough to start working.