Doesn't the existence of LVM snapshots slows down writing a file system wich doesn't support them natively?

As far as understand snapshots in LVM (please, do correct me if I'm wrong): since they are not persistent and work even with a file system which doesn't itself support snapshots => I suppose it must mean that as soon as a snapshot is active, LVM will takes a copy of every block which is written to, before it is changed; this copy is saved to a RAM cache and eventually ends-up in another disk-space; and each read from the snapshot will be diverted to this «cache» if it exists there. So I understand it means it should slow down every write while a snapshot exists. Does this mean that LVM snapshots should only be taken for as limited as possible durations, just for the time to backup data, and be suppressed as soon as possible ? And is this a concern only if the file system doesn't support snapshot natively ?