Start by just going out for walks when it snows so you start learning how the snow and weather and surface treatments all react and you start learning how to read the surface, I live in a fairly snowy area and there’s really only a few days a year when it’s so bad that i skip runs. Also trail shoes help.

My other tips are to never go up a hill your uncertain of going down and slow walk tight corners.

Just run. A dusting isn’t going to make you slip unless your shoes have 0 traction. I’d pay attention to when/how fast snow clearing is done where you live. I do not do speed work on the sidewalks (always have small patches of ice) in the winter just the road so i generally do it later when my neighbourhood is quieter. For shoes unless you are running on packed snow your regular ones are fine. If you might hit ice screwbies are a good option. For warmth just layer. Unless its truly frigid you probably won’rt need to buy too many winter specific things. The winter also has lots of good tips and tricks.

A dusting is probably fine and a good way to get used to it, and fresh powdery snow is amazing to run in, but snow can be a little tricky once it’s a day or two on the ground as it gets packed down, thawed and refrozen, etc.

I would take it easy, keep your feet under you, no speed work while you figure it out. If you feel like you need traction, you can get little cleats for your shoes. When I lived more rural, it was actually fine because I’d run in the road and they were usually plowed. Now I live in a city and nobody shovels their dang sidewalks so it’s really hit or miss whether I get out on the snow much.