Google Maps suggests heading north to I-90 then east to Billings then south thru Colorado.
I can speak to the route that far. I-90 is preferable to I-80 for lower average altitude and better road surface condition. (personal experience on these)

Yes there are passes you have to cross. No matter your route, you'll have to cross passes and if going in winter you'll have snow.

Interstates are graded as gently as terrain allows and are the first roads cleared in snowfall so - that's the route I'd take if I were you.

Be sure your vehicles are in good winter shape. Stay conscious of the weather forecast and try to choose a clear window to travel in if you can. (but your trip is probably too long to stay in a good bubble the entire time)

Good luck!