Horse theft was a pretty big deal. Here’s the basic Wikipedia entry: https://en.wikipedia.org/wiki/Horse_theft#United_States
I’m sure people stole buggies as well, but not to the same degree as horses.
When we asked my grandfather about my great great grandfather, Grandpa said, “we don’t talk about that old horse thief.” The census listed him as a dance-hall promoter.
Here’s a quick article about New York’s Mutual Association for the Suppression of Horse Stealing: http://blog.nyhistory.org/horse-thieves-beware/