Ah yes Ouray, CO and the Million Dollar Highway. Good road Very Steep and twisty in places but if you drive slowly and carefully you should have no trouble. There are several pull offs if you need a break. I drove it without a trailer in 2004. You didn't say what kind of trailer you have or what your pulling with. If your tow vehicle has a low gear make sure you're using it and the electric brakes are in good order. Test them & make sure they apply and release before driving that highway.
Many hairpin turns down to 15mph and some as low as 10mph.
Didn't say what you are pulling or driving. I have driven 50 from Montrose to Pueblo pulling my popup and love it. And Montrose to Ridgeway is a very easy drive. Just to note NO23putt noted, 50 is not the Million Dollar Hwy, that is 550 south into Durango. (Hwy 550 is more fun!)
Trailer: Lifted 228BH, heavy duty springs and Yokohama tires DELAMINATED ROOF TV: 2016 GMC Sierra Z71 4x4 CC, SLT
Spare TV: Two Alaskan Malamutes
Living somewhere in ID; previously lived in Moab UT; previous to that, don't ask!