Rabbits and snakes have no wings and parrots have two wings each, so there are $14 \div 2 = 7$ parrots in the zoo. Thus, the parrots account for $7 \cdot 2 = 14$ legs. Snakes have no legs, so the rabbits have $62 - 14 = 48$ legs altogether. Each rabbit has $4$ legs, so there are $48 \div 4 = 12$ rabbits in the zoo, as well as $24 - 12 - 7 = 5$ snakes.