Others have explained the sources of this effect: (1) you skin swells and (2) surface tension.
I wanted to add that this is very similar to a story I once read about Albert Einstein musing about beach sand. He noted that it is hard to walk in totally dry sand and also hard to walk in sand that is submerged in water, but easy to walk on sand that is wet but not submerged, right where the waves stop moving up the beach. He then explained his own observation: sand that is wet but not submerged in water sticks together through surface tension.
So this question has an excellent pedigree. I did some googling to find the story and I think this is it, but it is behind a paywall:
[https://physicstoday.scitation.org/doi/full/10.1063/1.2169417](https://physicstoday.scitation.org/doi/full/10.1063/1.2169417)
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