Small snails like ramshorn are not at all detrimental, in fact they are your best friend. Snails eat organics, including the fish poop which breaks it down faster for the various bacteria to then decompose it. And snails get places the aquarist never could.
As for numbers, they will multiply according to the food available. Obviously this can include food beyond what the fish need if we overfeed, but it is more the natural organics from the fish. I have pond snails and Malaysian Livebearing Snails in my tanks, and I'm glad they are there.
Ramshorn like pond snails lay eggs; you may see the egg clusters that look like gelatin on usually the underside of leaves, or sometimes on most any surface. You could scrape these off, but here you come to another issue...what to do with them. You cannot (or should not) just flush them down any drain or toilet; often these snails can survive in the ecosystem and that can be deadly for the natural fauna. So never flush or dispose in any outside water the snails or eggs, or fish or plants for that matter, unless absolutely dead. Fish and plant matter can go into the compost or organic recycling, or be buried, just so long as they do not get into the natural waterways. Even dead fish can pass foreign pathogens to the natural system because these are different for tropical and temperate systems.