No BBQ facilities (no cooking onsite) but you can still bring your own picnic. There are snack stalls but most of the food is junk food and whilst they did purport to have a KFC (not sure if it's still there) it was not actually cooked on site just brought in! Last time friends of mine went the snack stalls weren't open in the morning either (all they wanted was water). http://awpr.ae
If you do want to eat out nearby without breaking the bank there is the Al Ain Equestrian and Shooting Club which has a few restaurant choices and is a 10-15min drive away from the zoo http://www.aesgc.ae/