It is absolutely correct that Thrushes love snails; in with the Thrushes and out with the snails. Thrushes will seek out the snails, rummaging around in the borders and undergrowth until they find a tasty snail morsel which they will pick up and carry over to a smashing stone. Thrushes often use the same stone and will hurl the snail onto the stone till its shell cracks, and then snack on it. Nature is brutal, but more Thrushes means fewer snails and better looking Hostas.
Thrushes like gardens with food, so in addition to snails, shrubs with berries such as Cotoneaster horizontalis, Ivy, native Rowan (Sorbus aucuparia) Pyracantha, and Berberis darwinii are a few suggestions.
Frogs will also eat small snails and slugs and can be encouraged into the garden by water in a pond or boggy area and they also like wood piles. If you have no room for a pond, create a suitable habitat choosing damp shady area and plant with shade loving plants such as Ferns, astilbes, and Hosta to make an area frog friendly although this one in the image left joined me at the veg plot for a spot of slug spotting.
There are other predators of slugs which are also eaten by some types of beetle, slow worms, hedgehogs and toads. Thrushes will take the large snails but Black birds and Mistle thrushes will take smaller slugs, so the more wildlife in the garden, the better.
Both slugs and snails reproduce by laying eggs which you can find in the border as small white spherical eggs. They are often in the soil and disturbed by digging.