We drove past a funeral home in Vidalia, Georgia that has this horse-drawn hearse out front. I have never seen anything like it.
The glass windows were a surprise. Is that in case they were only "mostly dead"?
When I Googled images, there were dozens and dozens of different horse-drawn hearses and, yes, most had windows in the back.
But for the economy version, you might consider the bike hearse.
Or perhaps the side car is more to your taste?