As someone that had driven that route several times (though not in a u-haull), here are my 2 cents:
factors to consider:
day/time will you start?
how modern is your U-haul?
summer/fall/winter?
As stated in previous posts, you will cross mtns no matter what. If you are going during the summer, it will be prime road construction season so more delays can be expected. I found that out going to Yellowstone 2 summers ago. I would advise you to go north from COS on I-25 through Denver to Cheyenne, then west. Sure it can be windy but its only 5 hours across and it is more windy in the winter vs summer. Take the I-84 bypass and come out at Ogden and connecting with I-15. You pick up I-84 again an hour or two out of Odgen. Follow I-84 through Northern Utah, Southern Idaho, and Eastern Oregon. Near Hermiston Oregon, take I-82 north to Yakima and connect with I-90 for the remaining part of your trip. I have done the trip in 2 very long days (then again, it wasn't in a u-haul). If not entirely rushed for time, I would overnight in Evanston Wy, Baker City Or and drive the remaining portion on the 3rd day. That makes it for 3 regular days of driving. Stock up on CDs or find a way to play an iPod. There are some lonely stretches of the highway and radio stations are few and far apart.