There’s some thinking now that it’s actually an adaptive mechanism to help get better grip in wet conditions, like water-channeling treads on a tire: http://www.nature.com/news/2011/110628/full/news.2011.388.html. A major piece of evidence is that fingers with nerve damage do not wrinkle, showing that it’s under the body’s control, and not just a by-product of how skin is made.
But the fact that you do have to immerse other skin much, much longer would suggest that there’s an additional mechanism in the fingers and toes, wouldn’t it? I mean, water is still a hypotonic solution, and still going to permeate a permeable membrane like skin and cause some swelling, but the fingers do it so comparatively quickly…
In fact, I was just noticing yesterday while helping my daughter shampoo her hair (she can’t pour the shampoo from the bottle and catch it at the same time yet), that my fingers were wrinkly even though I was only touching the water for probably 2 minutes. Not very long at all - and certainly not close to “immersed”, as I was standing outside the shower reaching in.
All that, and especially the note that people with nerve damage don’t get wrinkly fingers…that’s some serious suggestion that it’s not just about osmosis.