I tend to go to several different parks in the city where I live and take snow and scenery photographs. Streets scenes can be fun also. I have slip on cleats for my boots. Good idea to have a spare battery. I usually take photographs for about 30 to 45 minutes, then go for lunch somewhere.
Another winter activity that's fun and inside, is to practice taking still life photographs.
My Canon SX100 from 2009 and my Canon SX510 from 2017 both take better quality photos than my cellphone. Both cameras also fit in my purse. Another plus is that my small cameras can be set to manual. Negative is that setting the iso above 400 results in lots of bizarre pixel stuff.
I have a Pentex DSLR and a Sony Nex-3. Usually use my Sony. But sometimes don't want to take my camera bag, etc. A small camera that fits in my purse is handy at times.