if you have the right equipment I imagine you'll be just fine, especially with a short commute like that.

Personally I hate riding in ANY kind of rain, kudos to you. IDK how you do it. Riding in the snow is pretty fun. You kinda glide over softer, newer coats of snow. As it accumulates you'll need studded tires - you'll go almost anywhere with those.

I have a beater bike (older trek commuter) that I keep in the basements for when guests visit. I throw studded winter tires on it and commute through the winters in Chicago with relative ease. I think the trickiest part is figuring out how to dress. It gets to -10 below zero or worse at times here, so you have to be prepared. It's great fun though. I love showing up to work on my bike in the middle of a snow storm!