No, syödä means to eat. But syötävä means something you can eat, something edible. It can also be used to casually refer to food, for example do we have anything to eat? - onko meillä mitään syötävää? or when inviting people over and offering them snacks and such, it can be called tarjota syötävää.
So in this case the reindeer are looking for food, something they could eat.