Carr &a Day & Martin make a good ointment for wet conditions that seals out moisture, it applies easily and dries to form a barrier.
Iodine or bleach! I think they also make some sort of copper that comes in a spray bottle? Either way you will be able to find something at a local tack store.
You just spray it on their feet after you pick them out. Bleach is a cheaper alternative (I can't remember how much it needs to be diluted so check that first).
People tend to not spray it on their feet before riding as it can mess up some types of footing.
I've had horses in super wet conditions and have used both. Bleach does just as good a job at maintaining the foot. I would talk to a professional or your coach/trainer before making any changes since they will have a better idea of your individual horse's needs.