We run the Jeep trails in that area often in a standard Jeep Wrangler and sometimes our pickup. (the milder ones in the pickup) Ridgway State Park is our favorite government campground in that area. Last summer we spent about a month at the Ouray KOA, which is very nice if looking for a commercial park. Actually the term, high clearance is used to let folks know that just having all wheel drive in their luxury sedan, may not be the best. However, most of the back road around Ridgway SP are fine for even two wheel drive pickups in the summer months. Owl Creek is a nice ride, as are some of the side roads off of Dallas Divide headed over toward Telluride. Until you get into the San Juan Mountains, do you need some form of 4X4, the shorter the better most times. How ever the back road tour companies out of Ouray, Silverton, etc. often use GMC Suburbans with the tops modified and go on most all of the back roads.
There are a few I wouldn't take any pickup on though, the top of Engineer especially if it is raining or snowing, Pokeepsie Gulch anytime, wet or dry, but most of the trails/county roads will be just fine. You may have to do a bit more backing and going forward more times to get around some of the sharp switch backs in a pickup, due to the length of the wheel base, but sometimes the clearance is a problem on any of the vehicles. I put some major gouges in the skid plates of my Wrangler last summer in western Colorado.
Ophir Pass, running from Red Mountain, south of Ouray over toward Telluride is another somewhat mild road with beautiful scenery. This switch back is one a longer vehicle will have to make a few back and forward moves to get around it, where as a Jeep sized vehicle can make the turn in one move. The country had moved the road from the far side of the valley, barely visible in the photo that was built on the talus rock slope. They couldn't keep the road where they wanted it so relocated it. Talus is naturally broken rock in piles. There is a cut through the snow bank on the left of the photo, just not showing.
Keep in mind and do read up on the Colorado laws in regards to driving on the back roads and trails. They specify how much lift is allowed on vehicles (high lifted ones tend to fall over and go boom on steep side inclines), the vehicle going up hill has the right of way, etc. Also since many/most of the trails are considered state maintained, they come under the laws regarding operating non-registered vehicles on them such as ATVs, UTVs, etc.
Some of the best maps and information is available at some of the Jeep rental businesses in the mountain towns. Some are free, some are for sale, or a person may want to rent a Jeep and not take a chance of recycling their personal vehicle. I have been known to rent a Jeep, even during the ten years we lived in Ouray, if I had busted my Jeep or didn't want to take a chance of busting it. LOL
Some of the back roads are just nice gravel roads, one being the road up to Animas Forks, north out of Silverton. Several of the old mining building still standing.
We had decided to go back to Ouray via California Gulch and Corkscrew but it was still mid June so we ran out of road before we got to the top. It gave me a chance to practice my backing skills.