Do you have the switch by the shifter on "W"? I don't think taking snow out of the tires will help because after you go back out in the snow it will just be exactly the same. Could be that there was ice under the snow there and it wouldn't matter what you did to stop. They had that video on the news last week where a couple dozen cars couldn't stop because of ice and ran into each other.
Letting your car warm up when it's cold out is always a good idea. If you know you have to stop, it wouldn't hurt to downshift to help slow down.
I don't envy you! I hate winter in MI because of the snow and cold, but I have too many roots here to change. Maybe when we retire.

Good Luck, and stay safe!