I'm 5'9" and my mare is 14.1 and I don't look too ridiculous on her. However, I have a very long torso/neck/head and shorter legs (really, I have the leg length of someone who's about 5'2") and Lacey, my mare (Arab) is rather wide.
Even riding western with properly long stirrups, my feet are only about an inch below her belly line.
So, in all, it really depends on how you're built and how the horse is built but I definitely wouldn't say that it's a foregone conclusion that you can't have an Arab becuase of your height.
Fabio - 13 year old Arabian/Lipizzan gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.