Maine here. We get snow anywhere from late October through April. Yes, 6 months out of the year!
I have never really had any issues with horses and snow. They go out most days as usual, but with more hay. If the wind is really strong and it's below 0 degrees before the wind chill, we will sometimes blanket them. The only conditions where we don't put them out is if its 30 degrees and raining. If the rain is going to freeze on them, but it's too warm to blanket, they stay inside.
If your horses are shod, you can get shoes with studs, or snow shoes for them. Regular shoes can be really slippery. I also make sure before I walk the horses into the barn that there is no snow balls/ice balls packed into the bottoms of their feet. That can make them slip on the cement isle way of the barn and hurt themselves, or roll an ankle. I just hang a hoof pick outside the barn, so I can pick the ice out before they step foot into the barn.
We usually make sure we have a lot of rough- first cut hay that has some tougher straw-like pieces. If you've ever put your hand inside a fermenting bale of hay, you know it gets really hot. That is what the hay does in your horse's stomach, so feeding lots of hay in the winter helps them stay warm.
"The barn taught me passion... Not the passion of winning-but rather the passion that you feel when you have nothing left but your love of something. The passion that is there when exhaustion steals your strength and frustration takes your hope."