It sounds like you've got a well broke ride there. I'm jealous! It's been many years since I last shot one from a horse. As I recall, it was at a big old west TX rattler and I was carrying my grandfather's SAA .38/40.
Regarding your question about a refinish: Unlike other forms of art (i.e. paintings, furniture, vehicles, etc.) firearms rarely increase in value when they are restored unless they have some significant underlying historical value. There are a few, and I emphasize a very few, artisans who can restore that M1926 to its original shipping condition. (The S&W Factory will not do it.) The value of such a restoration lies in the desires of the owner because the likelihood of ever recouping the cost of the restoration at sale is slim. A "kitchen table" restoration will only lessen the current value.
Here is something that I always try to remember if the gun in question shows only honest use and not abuse; The gun represents the desires of the previous owner and, as such, its condition is a part of its history. In the case of your handgun, the Houston officer felt strongly enough about it to trust his life to it. Remember, in the era in which it was used, an officer's sidearm was as much a part of "Officer Presence" as his badge was. A gun with "bling" like your's spoke volumes to someone who might cross him. If it were mine, it would stay exactly as it is. You have already found its greatest value when you touched off that first round!
I probably don't need to tell you but I would carry it with some form of retention like a thong or strap. They can jump out of the leather when riding in the brush or on a particularly skittish mount...(I can attest that searching for one after a long day's ride isn't fun).