On a serious note, going through a puddle is genuinely a valid way of avoiding trail erosion. The alternative of walking around a puddle means walking on the unimproved edges of a wet trail, which erodes that soil and makes the puddle wider. Continuing through the middle of the trail – puddle be darned – means the puddle might get a little deeper, but when it dries out, the soil will fill the hole again, by gravity.

Trails are not heaven-sent but are built and rebuilt every year by park managers so that the public can still enjoy a slice of nature, while balancing the needs of wildlife for undisturbed parkland. People that go trail walking after rain will know to bring deep boots, precisely so they don’t contribute to the erosion problem. Trail bikers also come prepared to wade through puddles, although they already tend to enjoy the mud anyway

As they say, there’s no such thing as bad weather but only bad clothes. Go forth into the puddles.

(Edit: to be clear, stomping on a puddle doesn’t do much to drain it. Some water will fly out, and that amount will drain away usually. But please, do not carve out a ditch to drain a puddle. Nature will evaporate it in time, or the park management needs to fix the trail drains)