I swim in an unheated outdoor pool in Spring (in the UK). It's cold enough to be uncomfortable but not dangerous (today the water was 14°C, and if it's below 10°C they close the pool). After a length or two, I'm used to the water temperature and my body doesn't feel so cold any more, but my head still feels as if I've been eating ice-cream too quickly.
Would wearing a swimming cap reduce heat loss through the head while I'm in the water? (I'm not worried about after I get out: I make a beeline for the hot showers.) If it makes a difference, I wear my hair about an inch long.