Our suggestion would be, go to Jackson, take 189 to Pinedale, thru Pinedale to Rock Springs, Which will put you at I-80. I-80 can be ugly at times. If you are experiencing weather, you can bypass Elk Mountain , by taking Hwy. 30 thru Rock River, MediceneBow ( where the book The Virginian was written). This route will avoid any serious mountain passes. I-80 can be ugly during the winter, but has more service (truck stops, rest stops, etc) than I-90. But, also has “much” more traffic (semi’s) to deal with! I-80 can often have lots of “black ice between Rock Springs and Rawlings, due to the southerly winds blowing snow across the warm pavement during the day, then freezing near dark!!!
Another option would be, take 189 from Pinedale to Farson, go to Lander (this “will” take you across South Pass , which can be ugly during a storm....but is a pretty drive) from Lander to Riverton, on to Casper. Once in Casper, you can take I-25 North to Buffalo, Wy. and there get on I-90 East ! You will likely have much less traffic on I-90, meaning......less fools to deal with.
If the weather has been favorable for several days, prior to your departure.....you can take Hwy. 287/26 from Moran thru Dubois, on to Riverton. However, this will take you across Togwotee Pass, which is beautiful, but can be ugly also.
All of these routes are very doable, provided you plan your trip between storms, your equipment preparation and your driving comfort!