As you know, no one can predict the weather conditions...just keep checking the forecasts as you travel and hopefully you have some leeway in time that you could hunker down a day or two, if needed.
As you leave Denver you'll have the Eisenhower Tunnel area on I-70 and the elevation is 11,013'. You'll have approx. 8 miles of 5-7% grades with 2 escape ramps.
You'll also have Vail Pass at 10,503' you'll have 10+ miles up to 7% grade descent with 2 escape ramps.
You will be at very high elevations and snow/ice can happen. Be aware.
Personally, I'd drop down and take I-40 across. Where did you want to go in Utah?