If I resided up in the Rust Belt, for sure and certain during the winter season, I'd be "stove'd up" trying to keep the salt, etc. " "warsh'd out" from underneath my vehicles.
Most likely, I'd have to do what some folks had mentioned and have a winter time beater truck/car.
Where I reside, sometimes in the winter months, there is an miniscule amount of snow(usually rain mixed with sleet)on the roadways, but it'll quickly melt and freeze overnight turning into ice.
We have trucks that will put sand down on roads and sometimes salt, but these folks down here don't have the experience driving in these type of road conditions.
... so, yeh it would be best to stay put. It usually isn't more than a day until everything has melted an safe to get out.