Never really fallen off in a puddle, but I did have a horse lay down with me in a tide pool on the beach before... It was the very middle of the ride (beach trail ride... I'm a guide) so I had to ride the last 45 mins soaked. :/
Bareback pads are not meant to be ridden in, even the ones with stirrups, as they aren't secure.
Better saddle up, or even do bareback, as any time weight is put in stirrups, this could happen. It gives you false sense of security I think, to have the stirrups.
I haven't done the mud thing, but wonder quite a bit walking across paddock cows come up into for feed, as last year trainer fell into 9 inches of deep mud. Not cute.
I really don't put weight in it..... I had for the moment to move up my stirrup on my foot. That's what they are made for, riding in. For you to have a cushion and to develop a better balance. And I was lacking the balance part. I said that. I use it for the balance lesson. I have suck moments in life. Lol.