Why do we have wrinkly fingers after swimming?
Great question, for which still no definite answer is known despite ~100 years of research. 

A simple physical basis for the wrinkling however seems unlikely as glabrous skin without sweat glands does not wrinkle, and as wrinkling requires the activity of specific nerves.

Moreover plausible evolutionary ideas, which used to be popular, such an anticipated improved ability to grab, don't appear that clear in newer experiments.

For the information above, and an even more detailed answer, please see Haseleu, Omerbasic et al. 2014 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0084949