It is extremely cold where I live coldest it’s ever been we had 16 inches of snow temperatures are 10° and less with the windshield. All of a sudden my car at high-speed‘s greater than 60 mph is shaking at the steering wheel. My BMW service manager told me to put my car in the garage she could be ice on that driveshaft and that it needs to thaw out. Could that be the problem I’ve had no weather issues since the weather got cold and the snow arrived.
If your rims are caked in ice, they are probably no longer in balance. Unbalanced wheels can vibrate the entire vehicle at speed.
I did this to my WRX playing in the snow one year, the entire thing shook until I cleared the snow and ice out of the rims. Same thing could have happened without drifting around an empty lot if you say you got over a foot of snow.
I would check those rims before worrying about the driveshaft.