Each kidney is a compact filter, the task of which is to pass blood through itself, leaving the necessary and getting rid of excess. The blood passing through the kidneys is purified and returns to the general bloodstream through the renal veins. Everything that has not passed through the filter (urea, uric acid, creatinine, ions and other end products of metabolism) is excreted in the urine.
In the cold, our intelligent body tries to keep warm and the peripheral capillaries shrink, therefore most of the blood passes to the internal organs, this is called the centralization of blood circulation. This increases the pressure in the kidneys and the amount of blood they have to pass. Consequently, the rate of urine formation also increases. Hence the desire to go to the toilet.