erm... This is not what's happening in the body...
To give you a general idea.
In a cold area, your blood vessel will constrict the reduce heat
lose. As BP = cardial output (your blood volume) x Peripheral
resistance (your blood vessel area). Your blood pressure(BP) have
to maintain and your peripheral resistance increased due to the
constriction. The only way to keep BP maintained is to reduce your
cardial output. Your blood volume contains red blood cells , water
and so on. So, water is removed to reduce your cardial output.
Therefore, your blood pressure is maintained. The excess water will
then be removed by urinating.
cheers.