Doc,
The two things that make Midnight Cowboy are the music (two incredible songs that are very memorable) and the acting of Jon Voight (career best performance) and Dustin Hoffman.
There are a few scenes in the movie in which the Voight character, who aspires to be a male prostitute for rich, horny old women, finds little success (mainly due to his extreme naivete) and is forced to look at some gay meat for business. In these scenes, although there is no actual sex shown, the look of repulsion on Voight's face with what he is doing is quite obvious. To the extent Voight became that character for that movie it was probably mentally tough on him.
The best scene in the movie is when he meets Sylvia Miles, a female prostitute on vacation in New York City. He strikes up a conversation, thinking he has found a horny rich older gal. Both Jon Voight and Miles think the other is a client that they have picked up on the street. They proceed to go to Miles' suite and have sex. After the sex, both Voight and Miles are demanding money from the other for the sex. It is hysterical. Best scene ever related to the hobby. Also shows early on how pathetically naive the Voight character is.