Actually, a variant of this is quite interesting.

There are three door, behind which are a car, a goat that always lies and a goat that always tells the truth.

You pick a door, but don't open it. The gameshow host then opens a different door to reveal a goat. You can ask the revealed goat one question about what is behind one of the other doors to which the answer is YES or NO (eg "is the honest goat behind the door I picked?"). However, you must write your question down before the start of the show, and the gameshow host is told what it will be (and can take that into account when, if you pick the door with the car, chooses whether to reveal the liar goat or the truth telling goat).

What question do you ask to maximise your chances of picking the car?

And if the goat says 'Mehhhh', does that mean yes or no in goatish?

Mehhhh.

I deduce: that you are not a car!

*giggles*

I was thinking more of performing horses, and having the goat tap one of two signs, on which YES and NO are written.

Of course, being a goat, it is more likely to eat the signs.

I'm sure there's a pun in there somewhere.

"Would the other goat say the car is behind the door I picked?"

Stick if the answer is no, and swap if the answer is yes.