I used to ride the horns a lot. Most of the people that go there book rooms at the lodges months in advance so a lot of times they are booked up. I usually would stay in Sheridan and drive back and forth everyday. Its about an hour from Sheridan up to Burgess Junction. Not a big deal since the lodges are: expensive, no cell service, very spotty internet, and the food sucks. Ive never ridden red grade, but from my understanding it is usually better late season?? I'm guessing there are a lot of rocks and not quite as much snow there this time of year.
Sheridan is a nice and fun town. The Wyoming Rib and Chop house makes a decent steak. A few different bars on main street that are all walking distance apart as well.
Make sure you guys have avalanche gear (beacon, probe, shovel, backpack). The bighorns don't get publicized as a big avalanche area, but i have seen a ton of slides there and everything open is usually corniced up. Maybe this isn't your first mountain trip? If not, sorry, just making sure you have the basics covered.