I got a special place in my heart for people who are crazy or broke enough to drive across the country to go skiing. I've done it three times myself via I70. You get a deeper sense of appreciation for the old saying "life's a journey, not a destination."
Looks like yahoomaps recommends taking the northerly route via 90, 80 then down 25 thru Colorado. But 70 could save you some tolls and might be a little less likely to get hit with snow.
Misc: If you're a meat eater, there a lots of relatively cheap steakhouses everywhere west of Miss river. Parts of west Kansas/east CO are so flat it's like being on a calm ocean (duh, it's a dried ocean bed). Should be no problem pulling in late somewhere and finding multiple motel options all along 70, if you don't intend to drive straight through. Borrow a radar detector if you can to embolden you to save 4 or 5 hours driving each way. New Mexican food is good, feisty stuff and a little different from generic Mexican. Seems like everything, gas/food/lodging, is cheap in MO and KS. Taos Ski Valley will live up to its tough reputation. If you're looking for a brief mid-point pit stop, the St. Louis Arch is next to the Interstate and has a free underground museum that would give your legs a good stretch (costs money and time to actually go up arch).