I can't say I have, but this is a common thing to see on M-185 given the non-emergency vehicle prohibition on Mackinac Island.
I haven't, but I grew up in Amish country so I knew plenty of people who did.
They also exist in some older cities. I remember horse drawn carriages being driven around downtown St Louis streets on weekend evenings until at least the 1990s. I've also seen them in other Midwest cities though it's been so long I can't remember which cities. I also saw some about five years ago in San Antonio around the Riverwalk and Alamo. However, the only time I've been on one was as a tween with my parents on Mackinac Island in the late 60s. I didn't drive it though.