Snails will eat attached algae, leftover fish food, etc. Some species eat plants too (mostly tropical apple snails). Contrary to what some believe, they do not eat fish waste or clean up the pond. Yes, they can eat some leftover foods, etc. but they also make their own waste. Some species of snails need a male and female (apple snails, trapdoor snails) but most are hermaphrodites (one can beget thousands). If you get a single pond snail in your pond, you will have plenty. It sounds like you already do. The best pond snails are the trapdoor snails because they are slow breeders. If you can get those, I suggest them. If not, I think black ramshorn snails are a pretty good choice.
Animals can carry in snail eggs or adults on their fur or feathers and transfer them from pond to pond. Snail eggs are often on live plants so if you add those, you often add snails. If the snails are native to your area or can survive the temperatures there, they will survive the winter. Female apple snails which are tropical (forget them where you live!) do need to come on land to lay eggs but the other aquatic snails don't need to leave the water.
My snail pages are at
http://www.fishpondinfo.com/snail.htmand
http://www.fishpondinfo.com/snail2.htm if you want to learn more.