After a break of 8 weeks I went into the cold water again. The air temperature was about 4°C, the water can't have been much warmer since it had been freezing all the nights before.
Following a tip of a friend I kept my hands out of the water to be able to stay in longer. It worked.
The riverbank is muddy, so I tried going in with Flip Flops so as not to soil my towel so much. Felt like Mr. Bean when I lost one...