Hi Jason from Pe Ell WA! Welcome to the forum!
That is a very nice 1860 Army. I noticed that the cylinder has very little roll-marked engraving left, but the bluing "patina" is very similar to the barrel. The frame is cut for a shoulder stock at the recoil shields, but it is a 3-screw frame with no 4th screw studs for the shoulder stock attachment. The wood is very good. The case colors are mostly non-existent on the frame, hammer, and load lever assembly. I am curious about that. The persnickety part of me notes that the wedge is installed upside down. The sole purpose of the screw above the wedge on the left side of the barrel lug is to retain the lip of the wedge spring when the wedge is driven out (right to left) for disassembly. There is
absolutely no need to remove this screw to remove the wedge, barrel, and cylinder for field stripping the gun. I have seen so many Colt guns where the wedge screw slot has been mangled, and there is no need for it.
The Colt letter is only good if all of the various parts on the gun show the frame serial number, all or in part. Such parts include the cylinder, the load lever, barrel, and others. The backstrap and trigger guard may have them, or have assembly numbers under the wood that match a penciled number on the inside surface of the wood. Otherwise it may be a parts gun. In the 1920's-1930's, when these guns were only worth pennies on the dollar, many small gunsmiths would swap parts between revolvers to create one that would work/function. I am not saying that is what your gun is, but I am just giving you a heads up as to what it might or might not be.
If you are a judicious individual, get a good set of hollow ground gunsmith screwdrivers and carefully disassemble it, grip frame first.
Take care!
To field strip it, use a plastic hammer/mallet to drive the wedge from the right to the left to clear the arbor (cylinder pin) slot. It will not mar the finish on the barrel lug. Put the hammer at half cock. Unlatch the load lever at the front of the barrel and use it to push the rammer against the cylinder face to move the barrel off of the frame locating pins. If it does not move readily you may have to let a few drops of penetrating oil where the barrel lug meets the frame do its thing. Remove the barrel and then slide the cylinder off of the arbor. Inspect and reassemble in reverse order making sure the wedge spring is on top of the wedge. Drive it in with the plastic mallet until the lip of the wedge spring clears the right side of the barrel lug. Cock the hammer and let it down on the nipple. Ideally you should then have only .001" barrel to cylinder gap.
If you wish to learn more about your 1860 Army, I would highly suggest Charles W. Pate's "The Colt 1860 Army Revolver" (2018) at about $60. I have a copy and it is a very good reference insofar as virtually all Colt 1860 Army revolvers produced. He has, among many other things, shipping information about them.
Insofar as cleaning, DO NOT use any acid based cleaners (such as vinegar) as it will remove any bluing/case colors in a New York minute. Only use alkaline cleaners. HOT water and soap, followed by a liberal application of Ballistol or similar will work well.
I only wish I could afford an original. I am 67 and on SS so I am relegated to collecting Italian replicas, primarily Pietta 1851 Navy .36 "type" pistols, to include many replicas of Confederate revolvers.
My Armi San Marco 1860 Army (BC 1993) 4-screw cut for a shoulder stock with the original ASM round cylinder and an Uberti full-fluted cylinder. I don't know what you paid for your original 1860 Army, but I only have $300 into my replica.
Jim