The easiest route with bad weather is to take 70 past Vail and Edwards to Wolcott. Then grab 131 straight North into Steamboat. I have taken this several times from Vail for a day trip to Steamboat.
No passes, no switchbacks, and pretty flat and boring.......but I prefer boring to Rabbit Ears and Berthoud!
Have plenty of gas and a strong kidney

, there is nothing in between Wolcott and Steamboat.
This would also be the ideal route from Eagle airport. Wolcott and 131 is between Eagle and Edwards.