This can be alarming. Try to avoid it by wearing rubber-soled shoes in wet weather (or wellies, or even galoshes over your shoes). Leather soles and their stitching will soak up water.
If you get caught out, water may seep up through the welt-stitching around the sole and appear, particularly around the toe-cap and vamp. The heel and quarter are generally held far enough above the water that they get off with it!
When this happens, get the shoes off and leave them to dry as soon as possible. Wipe off any mud etc with warm water, stuff them with newspaper if they are really sodden, but …
Do not be tempted use a hair-dryer or stick them on a radiator or hot water tank!
Lay them on their sides in a warmish, dry place for as long as it takes to dry them out completely. The toecap and vamp will be the last to dry.
You may then see something like this image (not one of my Loakes – I try to keep them from the floods!).
I know – it looks horrible. Wipe off any white stuff (probably salt from your sweat!) with a damp cloth.
To reduce this nasty effect, treat them to a good coating of neutral or appropriately-coloured shoe cream. Lave it to soak in and if it seems to do that quickly, apply another coat. Several thin coats are better than a huge slathering. Then polish them with a cloth. If you can still see the water stains, do it all again and finish off with a nice wax polish.
If you have been slightly over-generous with the cream, you may find that some of it is forced out of the leather at the creases as you walk. Just wipe it off – it’ll stop doing that when the leather reaches equilibrium.
Hopefully you now have a pair of shoes without nasty marks and you can regard any remaining faint markings as a contribution to the shoe’s patina and part of its heritage!