What does it mean when you call someone a one horse pony?

It means you are quite a character, like Yogi Berra or Sam Goldwyn.

That means that the pony likes or loves only one horse.  It's like the two are meant for each other, like marriage.

It means the person that said it is senile.

First of all, the expression is, "...one trick pony."  It means that the person referenced handles all situations in one manner, a sophisticated way of stating that someone is predictable and/or stupid. 

That is what the moron Biden called a reporter this week.

It's one trick pony.  Guess the Kremlin wasted it money on English lesson with you

A one trick pony.