Haha-- When I repeated the horse/Mayo joke to my husband, he immediately thought of that movie, too. He also said something about there being a wall full of mayonaise jars behind the doctor at the Mayo clinic.
I bet everyone who works at Mayo clinic has heard every mayo pun there is.

Lagrange, when my husband goes on break from work, I will ask him to explain the punch line you wrote...I still don't get it.