What normally takes 4 hrs, through yellowstone park is closed during winter....... 8 to10 hrs depending on roads......Go from Cooke to Gradner MT, to Bozeman Mt, to West Yellowstone Mt, to Inland Park Idaho, to St Anthoney Idaho,,,If your not pulling a trailer from St. Anthoney head east to Driggs Idaho than Victor Id. and over Teton Pass (no trailer allowed). Your now in Jackson Wyoming, at the 1st 4 way light turn left head north out of town for approx 60 miles on hwy 26 and your at Tog.
If you pulling a trailer you'll have to go to Rigby Id, take the Ririe Idaho cutoff, going east toward Alpine Wyoming/Jackson Wyoming. The longer way adds an hour to your travel time....
I don't think the road from Cooke to Pilot Butte parking area is passable with trucks anymore, if it is go through Cody Wyoming through Thermpolis Wyoming to Lander Wyoming to Dubois Wyoming and up to Tog.
Anyway you look at it it's a good haul
OT