In a word, yes.
Its not the water so much as the mud, which will grind around inside, all over your nice shiny copper / carbon commutator / brush bits. It also won't do the bearings any good. A quick flush with corporation pop will help after each dip in mud.
Second, running any machine flat out will shorten its life, but I think your battery would have gone flat first rather than managing to fry the regulator circuit on the alternator through overuse.
A third observation is that if the first replacement was for the 1992 original part, and the last two were of the budget persausion, it could be that you are reaping the rewards of inferior parts?
If you hang on here a bit several adults will recommend good makes, and also that if you take yours to the local motor electrical specialist they may be able to fix it or part-ex it for a good one.