You definitely will have less range in the cold and knobby fat tires also reduce range. If that range will be less than required for the commute, you will have to investigate.

If you leave the battery outside, it may even be too cold to start. While riding the battery resistance will generate some heat, but that only when it wakes up to begin with.

Some batteries deal with that better than others, but on a cheap bike don't expect NASA type technology.