Even when I-80 is closed, it's never for long periods of time. Longest I've seen recently was over Christmas this past year, closed between Rock Springs and Laramie for about 2 days. Just come prepared, and budget for an extra night or two in a hotel in case you need it. You'd be fine in a car through there... biggest issue there is wind reducing visibility and making it tough on high profile vehicles and the road icing over, and tires don't help much with ice.
I'd also advise staying in Rock Springs over Rawlins if you do get stuck and have a choice. More hotels and more things to do.