Howdy Mark,
You must be leaving from Lost Trail Ski area, correct? One of these days, I'm going to do a WTW TC Road Trip to some of the smaller ski areas in MT and ID. Maverick Mountain and Lost Trail are on my list.
I suppose you'll cut through the Big Hole on the way from Hamilton to I-15 enroute to SLC. If you haven't seen the Big Hole, by all means take MT 43 to Wisdom, then MT 278 through Jackson to Dillon and I-15. Incredible alpine valley. There's a hot spring pool at Jackson Hot Springs resort, along with a very nice restaurant and bar.
In 2011, I road-tripped from Park City to points east, and simply because I'd never been that way, we took US 40 through Heber City, Vernal, Craig, and Steamboat Springs. We went on through Rocky Mountain NP and avoided DEN, but Trail Ridge Rd is of course closed until late May-early June. I have read somewhere that the I-70 eastbound tube at the Eisenhower Tunnel is being worked on and there are/will be heavy delays for a few months, to you might want to check that out on the CO DOT website. I suppose US 40 over Berthoud Pass would be the option, and if you're not in a hurry, why not?
Leaving Heber City, UT headed east on US 40, you'll climb through a pass and will reach a huge open area around Strawberry Reservoir. That looked pretty nice to me. There are a bunch of back roads and trails along the CO-UT border near Vernal, and being low along the Green River there might not be too much snow there now. It's pretty nice heavily-rolling mesa country between Vernal and Steamboat and lots of side roads through the Western Slope ranch country. There's a nice public natural hot spring complex just north of Steamboat called Strawberry Park. It's open at night, I believe, and it's got a rep as a very fun place to hang out after dark (no pun intended). If US 40 east of Vernal isn't appealing, or if getting over Rabbit Ears Pass east of Steamboat looks bad, you can head south to Rifle through Western Slope ranch country (through Rangely?), then turn east to Glenwood Springs and have a soak at the big, nice outside hot spring pools there.
I'd be very tempted to snag a ski day at Deer Valley on the way past Park City, and a real hidden jewel is Sunlight, not far from Glenwood Springs. I'd surely have to see how the conditions were at Copper Mountain, too.
Have a safe trip and do post a TR and some pics.
Foy