Snail populations are limited by the available food supply. If you're having a population explosion it means there is too much snail food around. You may be feeding too much or not vaccing enough. Most methods of controlling them will be temporary unless you can figure out the root cause.
Loaches are notorious snailkillers. There are large species, like Clowns; medium species, like yo-yos; and smaller species, like zebras and skunks. Temperaments vary, but they're mostly nice, interesting, playful fish. Check out
loaches.com for more info. They're bottom-dwellers so they may skirmish with the cats.
The easiest non-fish method seems to be putting a piece of lettuce on the floor of the tank in the evening. In the morning it should have a whole bunch of snails under it. Discard, repeat as necessary.
But if you don't figure out why they're there in the first place, they'll be back.
HTH
EDIT: I'm agreed with Richer below on snail-killing chemicals. I wouldn't put them in my tank for love nor money.
EDIT: Agreed with Kit below as well. Clowns get big. They don't belong in little tanks. Big loaches in big tanks, little loaches in little tanks. Also bad to overcrowd the bottom.