Technically a rain garden is supposed to drain within about 24-36 hours, so it doesn't have the standing water that mosquitoes need to breed. If you have pouring rain for a week or more so that it stays full, you might want to check for mosquito larvae; but mosquitoes need still water and driving rain is definitely not that.

A wildlife pond may have mosquito suppression in the form of fish, amphibians and their spawn, dragonflies, and/or various types of mosquito dunks that are wildlife-safe.