Yeah, the snow is only a problem if you're wading around in it (which isn't often unless you're going out to play in it). The wind and cold is what makes it uncomfortable to go around outside. Scarf, hat, gloves, and winter coat are a must almost immediately. Without them you'll be very uncomfortable for anything more than just a quick jaunt from the parking lot into a store, and in physical danger if your car broke down or got stuck or something and you were in the cold for an extended period of time.

The biggest thing is keeping cold wind off of exposed skin. Scarf and hat the covers your face and ears, gloves, a jacket that insulates, and thicker pants that block wind (or especially long underwear). This is what keeps you warm.

The biggest thing you'll learn is how to dress in layers. You need to be able to add or remove layers depending on what you're doing and the weather. Fully bundled up and shoveling some snow with no wind and the sun and you'll quickly overheat (I've sometimes shoveled snow in boots, jeans, and a long-sleeve shirt) but add no sun, wind, and blowing snow and I'll be out there looking like I came from the arctic.

Overall it's an easy skill to learn; just make sure you have some of the basics and you'll quickly adjust.