Best Shoes for Winter Running?

I’m new-ish to running, and this is the first winter that I’ve been consistently running outside. Generally, I’ve just been running a little slower to avoid slipping. At the end of January, I’m going to be running a winter half, which could include snow and maybe some ice. I’d like to actually race it without falling, but I have no idea what the conditions are going to be.

I’m curious what other runners do for winter road running in colder climates. Could be a stupid question, but is it common to wear trail shoes on the road? Or are there specific types of higher traction road shoes that are worth buying? Any recommendations? Thanks!