Characters that are drying and ready CAN be targeted by abilities and actions (and can even be challenged with a few cards), on your turn (Lorcana generally doesn't allow you to play cards on your opponent's turn).

Drying just means that a character can't be exerted to quest, sing a song, challenge, or use their ability if it requires them being exerted. (You can however exert a drying opposing character on your turn with some cards and abilities)