I often here this on TV. Mostly it is the character reading a letter going…blah blah blah…And the horse I came in on…Then they get made.
What is this?
Well, the full phrase is “Fuck you and the horse you rode in on”. So, on TV where they can’t say “fuck”, the joke is that they’ll have the letter end with the reader partially reading the last time ("…and the horse you rode in on") with the expectation that the audience knows what came before. You see this, for example, in the Simpsons episode where Roger Myers Jr. replies to Marge’s letter.
However, I don’t know when or where the full phrase originated.