Do I make the first move or wait for him to do so?

If he is "arrogant, snobbish and kind of cold" then why on earth do you want him? If the last thing you want to do is " boost his already huge ego.. " do not make the first move, ever! To be strictly honest he sounds like a player and if he feels out of reach, then your gut feelings are trying to tell you something; do you want him for him, or as an ego boost/arm candy?