This is not very likely for a variety of reasons. First, most people in the American West did not have a horse. The West was highly urbanized, and maintaining a horse in a city was extremely expensive and largely unnecessary. It was easy to walk to most places, and they actually had fairly good "mass transit" - omnibus horse-drawn coaches within town, and stagecoaches or railroads for out-of-town trips. Horses were the property of the rich - who often had their own stables - of businesses that needed horses, or of farmers/rangers who needed horses for their occupation. Large communities usually had stables where one could "park" one's horse for a fee - but it was worth it because they were fed and cared for - and there was that matter of security. Smaller towns - where a rancher might visit with his horse - might not have an established stable, but in that setting, it was more likely that everyone would know one another - and recognize one another's horses, so getting away with the theft would be more difficult.

I address the subject of horses and urbanity in my book Virginia City: Secrets of a Western Past (2012). This thirty-year retrospective of my career dealing with the material remains of the past includes the observation that horse-related artifacts were extremely rare in the many excavations I supported.