Before you all get worked up on it, I'll say this. All cutthroat are the same species... you are trying to identify the sub-species. This can be very difficult. You will find that characters will overlap between them all. Here are some suggestions to help you figure out what you could be looking at.
1) Get Dr. Benhke's book on Cuttroat trout. This book will not help you see them historically, but also give you an idea of characteristics to look for. Pigment concentrations or evenness, pigment in the fins, or even the number of gill rakers.
2) Take note of the watershed or drainage you are in. Yes, Greenbacks are native to the Eastern slope and Colorado River Cutthroats are native to the Colorado River Drainage (hence the name). Rio Grande Cutthroats are from... yes, the Rio Grande River Drainage.
3) Look for signage. Most of the places that fish were stocked could be remote and have specific signage or details. Joe Wright reservoir as an example.
4) Check the regulation brochure. There used to be some locations that you could actually harvest cutthroats, including the greenback (limit was 2).
These should be some keys to help you identify (or narrow down) your specimen of cutthroat trout.