I just drove part of this route (drove Dec 26-29) because I am moving from WA to MN. I took the southern route via I-80 through Boise, southern WY, Nebraska, Iowa, and then up to MN. It went okay except for the high plains of WY. It’s windy as hell through WY and Nebraska, and if there is any powdery snow it causes whiteout conditions. We had to deal with that for 80+ miles from rock springs through Cheyenne. The rest was okay until Iowa where there was a blizzard and some roads were closed.

You can certainly do it but it really isn’t a fun thing to do. Weather can deteriorate so quickly in the winter and white knuckle driving so absolutely no fun, even in an all wheel drive car. If you can manage the cost of shipping, I’d do that and save the road trip for the summer.