it's when your feet submerge at the bottom of the stroke that concerns should be raised... wet feet in winter isn't much fun. But the bike should be ok getting wet. You shifting problem is just a bit of gunk somewhere on the shifting mech. A clean should sort it.
Not too deepYep. My last crash (May last year) was caused exactly that way. I was going slow, but still managed to get a nasty gash on my shin (must have been the pedal that caught it).
Pretty sure I freewheeled where possible to avoid wet feet.
View: https://youtu.be/Gj2sg-luZAw&t=38m
But my first attempt at fording I ended up grinding to a halt in the middle of the ford and had to put a foot down
