Slow Down (You may have to anyway!)
While you can make the 1800 mile drive from New York to Denver in three days, I'd hardly call such an endeavor romantic especially if you're going to try to push a couple of tons of RV across America in that time frame.. I also think that 7 days around Colorado is pretty much a minimum for a low key visit, and even then you're going to have to pick just one section of the state. So, my first recommendation would be to add at least 2 or 3 days to this trip. 13 days (what you've got tentatively scheduled) is an odd number (besides not being even) in that when most people take a two week vacation it's usually 16 days when you add in the 'extra' weekend. I'd really try to scrape those days together if you can.
Then with 4 days each way, you can travel some roads other than I-80. Just a few that I'd suggest you look at are US-40 through western Maryland, US-52 down the Ohio River, US-54 and US-400 across southern Kansas on a 'southern' leg and US-6 across northern Pennsylvania, US-62 through Ohio's Amish country, US-6 again along the upper Illinois River and US-30 along the Platte River in Nebraska on a 'northern' leg.
I don't know about the specific Dude Ranches in Colorado, but we do have a couple here in Arizona that I've been to and typically they have riding programs for horsemen (and women) of all levels of expertise, including someone like me who's never been on one before.
AZBuck