There are lots of places off the roads that are both accessible to the public and by horse. Start by getting a Glenwood Springs Surface Management Status map from the BLM. From the Dotsero exit take the Deep Creek Road up the Mountain. Find a place to park on BLM ground on the way up and take one of the closed two track roads off the switchbacks and you should be in great mule deer country for the 3rd season. If you can get around up top (you should be able to unless it snows too much) park at the Coffee Pot campground and ride south on either of the 2 forks until you hit a dead end, then keep going. This is sheep grazing country and you can get around on a horse almost anywhere.
If you can find somewhere to park the truck and trailer you can ride the horses up Transfer Trail from Glenwood and find a place to hunt--ledgy country, but doable if you get up far enough.
Don't expect much for trophy quality, but there are some respectable bucks around, and a few elk too. You never know what you'll run into, especially in November.