Why is water leaking near my bathroom's exhaust fan?
You may have condensation running down the vent pipes into the fans; given how a vent pipe attaches to the back of a fan, the condensation will tend to run to the side(s) of the fan fixtures.


Are the vent pipes uninsulated and in a cold space?
Could condensation have frozen inside of the pipe, and then melted at the same time as the snow?
Would the snow have stop the wet air getting out of pipes?


If it is condensation then you need to insulate the pipes and/or add a condensation trap just above each fan.

Assuming that all 3 exhaust fans vent via different pipes, you are looking for a design fault, as I cannot think of anything else that will be in common between all 3 fans.