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In fact, I'd take all Interstates - I-35 to I-135 to I-70 to I-25 to I-90. That's only 2260 miles, overnights in Hays KS, Casper WY, and Butte MT if weather cooperates. The E-470 toll bypass of Denver is cashless, license plate tolling, they mail you a bill ($13.25). If it's not rush hour, you can use I-270 (free) instead. The I-35 toll in KS between OK and Wichita accepts cash ($2.25).
Hays has a bunch of motels ranging from lower-priced to the upper-middle end. Moab, not so much -- tourist town! So many folks there trying to see Arches and Canyonlands, that raises prices, even at the end of January. Add in the fact that you're traveling on a weekend ... up go the prices in Moab, not so much in Hays.
Donna
I will say, no matter which way you go (and I would agree with the all-interstate route suggested by GLC as my first choice as well), make sure you are keeping an eye on the forecast and staying flexible.
If the weather looks clear, and you decide to stick with your route through Moab, make sure you double check the forecast before you leave Santa Rosa and make sure that section still looks clear. Worst case, from Santa Rosa, you could still cut up to I-25. Similarly, if you take the route suggested by GLC, double check the forecast somewhere between Denver and Cheyenne and make sure I-90 still looks like the better weather route, and consider taking I-80 across Wyoming if the weather looks bad in Montana. If all things are equal, or the weather looks like it could get bad on both routes, then I'd stick to I-90, because it stays at a lower elevation than I-80.
The problem with I-80 across Wyoming, besides altitude, is it crosses a lot of open plateau. It's subject to high winds, blizzards, whiteouts, and black ice. It closes a lot more frequently than I-90 because of this.
Real time road conditions for all states are at safetravelusa.com.