Why do you warm up over time?
Fundamentally, for the same (broad) reason we mammals don't have to wait for warm, sunny days to get anything done?
First, of course
(ETA: during warm weather*) if the water is at or above ambient air temperature, you probably won't feel cold to begin with (except for perhaps a
very slight chill due to the evaporative cooling affect of soaking yourself if there's any air movement to speak of) because your skin's temperature will already have adapted to that. But even if the water is cool-but-not-really cold, thanks to natural selection, the capillaries in your skin will dilate pretty quickly to allow greater blood-flow to it (and the rest of your homothermic circulatory system will do what
it does to allow that to happen). But otoh, if the water is
really cold, you won't ever really warm up, and in fact will probably die trying...
ETA: Strictly speaking if the water temperature were the same as the air's, you would probably feel slightly cooler a few moments after you got into the pool, but before your circulatory system did it's thing, because water is a much greater thermal conductor than air.
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* I briefly forgot where I was posting and so naturally assumed we were talking about people who don't generally jump in swimming pools when the air and/or water temperature is/are ≤ 32°F, or even 65°F, for that matter.. I know, I know... silly me....