Over the years I have refinished furniture that has been handed down in my wifes family. Any thing that was stored outside needed at least 3 times the re-work Inculding new veneer, and new solid wood pieces in the worst of cases. Seems to mostly affect any surface that was stored horizontal to the ground? IE.. tops, connecting pieces that are horizontal etc.
My recomentation is that you do one of 2 things.
1) If the speakers are of Heirloom quality, store them in a temperature controled area, if need be in your current apartment.
2) If not sell them, and once you have your dream home go buy a pair in super good condition.
I say this because between the Veneer and the MDF those two products absorb moisture at different rates and after a short period of time the gule will loose it's hold. most likely in a garage you will need a new veneer job if left for more than a few seasons.
My comments above assume that the drivers will not be affected, and that may be another story. As rust likes to quickly grow on metal magnets. This will likely build up in the small slot that is occupied by the voice coil, and then you have have a big mess.