I was going to post links to my dashcam vids of some of those roads in winter but MM's point about Yellowstone being closed suggests that the purpose of the trip will fall away leaving no reason to go there.

I drive I-25 and I-90 in a Jeep from Colorado to Seattle for Christmas. I have needed 4WD in winter for portions of every trip in each direction. (needed it in April this year too) The interstates are plowed and sanded more quickly than other roads but sometimes it seems like the plows aren't actually helping when they just polish the ice. The semis will then chop up the ice with their tire chains making for a pretty rough, and slow, ride.

I have a 14 year old phone with service with T-Mobile. I have no service in Montana or Wyoming. Coverage depends on your carrier.

Passes eastbound- Snoqualmie, 4th of July, Lookout, Homestake, Bozeman . There are traffic cameras each state has connected to the internet so you can see what conditions are from your 'net connected device. Lookout Pass is about the steepest grades of the group. Even in good conditions you still might cross it at 30 mph because of the slow truck traffic.

Winter essentials- reliable vehicle, new wiper blades, washer fluid topped up, good (deep tread) tires, warm clothing, shoes or boots that won't freeze your feet in the snow in the parking area, blanket or two,ice scraper, ice melter (windshield washer fluid in a spray bottle works for less $). $$$ to pay the towtruck driver if you break down or screw up and slide off the road.

It's all completely doable but it's best not undertaken lightly.