Nick I drove OTR for 4 Years and once you get Over Donner and out of CA the roads are not normally not to bad in winter. The only other 3 you will have worry about are Parley in Utah just East of Salt Lake City but they keep it Clear. Elk Mountain in Wyoming and Sherman Hill in Wyoming also. However if you see the Trucks are taking it slow on them Watch them.
Also remember to pack the heavy items LOW in the Uhaul so you have weight low in the truck and put a few items that are heavy on the back side to get some weight on the tail. Just take your time and you ill be fine heck I did more time on I-80 in the winter than I care to think about in all kinds of weather. The Interstate to sta the HELL OFF in Winter is I-70unless you like playing at over 10K feet with major Grades and avalaches that will bury a freaking truck in a hurry,