You're better off with a uke going from a drier to a wetter climate...as long as it's not raining on the poor thing! What can happen is that the wood takes on more moisture and swells a little bit which could make the top belly up, thus raising the action a bit. You can also find the neck reacting, and that can lead to fret buzzing, particularly if the neck back bows a bit. Usually, though, it's just tune and play, and if the playability seems compromised, then take the uke to a luthier for a setup.
Wet to dry...that's where you have to watch for cracks because the wood shrinks, and if the top or back were made without any doming then the sides can restrict top or back shrinkage, and then something must go...and it's usually along the weakest grain lines in the top or back, and it will crack. This is not uncommon with tropics-built ukes going to US mainland desert areas or to the north or east where winter heating dries out the air quite horribly for delicate wooden instruments. That's where humidification is a must. Most builders will not cover dryness induced wood cracks under warranty, and rightfully so.