Bighorn sheep are common in the park. They are usually a little skittish, but without making any sudden movements or noise, it is possible to get some good photographs
If you want to see elk in the wild, Rocky Mountain National Park is the place to go. During the winter they even get into the town of Estes Park, just outside Rocky Mountain National Park. During the summer, they tend to tuck themselves back into the forest, but it is still likely that some will be spotted on every trip. The waterfall was the attraction for these elk.
Somebody offered to take a photo of my wife and I, overlooking the alpine tundra at an altitude of a little over 12,000 feet. It was cold and windy that August day, temperature in the low 50's.
The little whitetail kept moving in and out of the forest. It would take a drink at the stream, and then hide again. The elk didn't care who was watching, for how long.
Rocky Mountain National Park attracts many trout fisherman.
Horseback would be a great way to see the Park.
For information on Rocky Mountain National Park, visit my Squidoo lens: http://www.squidoo.com/rockymountain