The worst you can do with some good leather boots is to dry them too quickly. The leather will shrink and probably split.
I have a good few pairs of boots which I will cycle through if they get wet, while they dry out slowwwwly. Newspaper inside, just in a dry, room temperature area.
If they're already completely soaked, a hard brush under a tap and get ALL the mud and crud off them. If they're just damp and mucky, it can be easier to let them dry and then dry brush the soil off.
Ledergris is good stuff, definitely more leather life prolonging than your typical Kiwi/Cherry Blossom polish. A decent treatment will provide better water resistance than a dried coating of mud.