Normally, WX-78 should always take some amount of damage if they're wet at all, but this doesn't happen if it's not raining. They can wear a Fashion Melon or Ice Cube or just passively dry off without problems.
If it's raining though, even if WX-78 is fully protected with an Eyebrella they will take damage from drying off, as it was intended.
Get wet in any way when it's not raining and try to dry off, no damage either way. Get wet in any way and wait for rain, WX-78 takes damage. Wear full protection so you can dry off, WX-78 takes damage.