In addition to what Cathy said, here are links to the Department of Transportation websites for Idaho and Montana. Usually the Idaho ones are updated by 630 or so in the AM for people going to work. I don't generally look at the Montana site, but would guess by early AM there would be a current report up. Both sites have webcam links as well altho I don't see any webcams on 191. Both sites have a whole state map of how driving conditions are at the time, so play around with both sites before you go.
Here is a link to a webcam in West Yellowstone. If you go to the Webcams link on that page it will also take you to links to other cams in the area. The Island Park area would be on your way from Idaho Falls to West Yellowstone.
You also would obviously check the weather locally and regionally before you set out from Pocatello. You can find Winter Weather Advisory lists and Winter Weather Warning lists of specific areas on weather.com.
Edited: 10:33 am, November 26, 2013