Hello again. Estes Park is the town literally adjacent to the eastern side of RMNP. You will be going up to Estes Park by about 2500 ft. from Fort Collins. You do not want to miss Rocky Mountain National Park. It is an easy day trip from Fort Collins. I do it all the time from Windsor--I have a Fort Collins zip code.
There are actually only 2 horseback riding stables inside RMNP. Sombero runs both of those, Moraine Campground and Glacier Basin. The other stables begin their rides from Estes Park and some ride into RMNP or Roosevelt National Forest.
You do not need a horseback ride to see amazingly beautiful scenery and wildlife in RMNP. One of the great things about RMNP is just how accessible it is. The roads through the park with all the overlooks and pullouts, picnic areas and short easy trails provide access to waterfalls, alpine lakes, high mountain peaks, huge granite monoliths, wildflower filled meadows (usually at peak around the first week of July) and great chances to see wildlife. Even if you want to take a horseback ride, plan to see areas of RMNP the horseback ride will not cover.
The first week of July is absolutely the busiest week all year in Estes Park and RMNP. For that reason, I would choose a ride from stables outside RMNP and Estes Park. Check out Sombrero's Allenspark stables. They are in a less visited area of RMNP (if there is such a thing the first week of July). This is an area (Wild Basin) you would not see from the roads in RMNP.
If you need a fun day trip from Fort Collins to RMNP without a horse, I can give you an itinerary.