Do you want this automated, i.e. when a car approaches the gate automatically opens?
Another reason I ask is there are many
relays controlled via a keyfob (you would need to add a 12 volt coil relay and 12v wall wart) so you could just press a button when you approach.
Another cool thing that I've wanted to implement but never got around to it was use something like a
flash2pass or
tap2pass technologies for something like this. (
HERE are some Amazon links)