I-90 or I-80 Omaha>Portland in December?

I'm moving to Portland for school in late December. I'm looking for advice on whether to take I-90 through S. Dakota and Montana or I-80 through Wyoming and Utah. I would love to have one last Christmas with my family- but I start classes on Dec 28th. Is it even possible to battle the snow and mountains in that short of time?
I'm also looking for advice on whether to rent a U-Haul and tow my '89 Civic or to ship my furniture.
This whole endeavor seems like an expensive and time-consuming headache either way. Any suggestion would be greatly appreciated!

Welcome to the RTA forum!

It really is impossible to know in September, what weather you might see in December. Trying to guess more than a couple days out is fairly pointless endeavor. Either Route could be completely fine, either or both routes could see a snowstorm during the specific time of your trip.

In any case, I would plan to celebrate christmas a little early. You're going to need a good 3 days to make the trip on either route, and I'd want to have at least one or two extra days in case you do see some weather that forces you to slow down or even stop for a day.

You'll have to price out what options might be cheapest for moving your stuff. I would also look at how much your stuff is really worth, and if it might not be cheaper for you to sell it or store it, and then just buy some replacement items when you reach your destination. If you don't have many things or they aren't worth much, that could be a cheaper option.