That sounds mighty damp. Have you already overwintered your bees on solid floors, and had problems caused by dampness ? If you have done so, and all was fine, then I’d put the trays in. Otherwise, I’d leave them out, but I’m assuming your hives are well protected from those winds. If they’re not, then add some skirting so that the wind doesn’t blow straight up into the hive. Another possibility, if your tray has a lip around 3 sides, is to put the tray in upside down. This will give extra ventilation under the entrance, but protect against the wind. (Make sure the hive is tilting slightly forwards).
And now, just thinking out loud on something I know nowt about, could those mists & fogs coming off the sea contain salt water, and if so, could the salt prevent any spores from developing in the hives? Perhaps someone who knows about this sort of thing could put me straight on that ?