This is absolutely true; you do pee more in the cold!
The reason is that in order to minimise heat loss during cold exposure the body restricts the flow of blood to the skin and superficial tissues. This is called peripheral vasoconstriction. The result is that blood is shunted to the body core, the volume of blood circulating in the core is higher, and mean arterial blood pressure is higher.
Blood volume, and hence blood pressure, are regulated by the kidney, which either reabsorbs or sheds water from the body according to how well hydrated we are.
So when you are exposed to the cold and your blood pressure rises, the kidney interprets this as due to an excess circulating volume, and sets about losing salt and water in order bring down the blood volume and hence blood pressure. As a result you produce more urine, just as you observed.
Medically this is referred to as "cold diuresis" and it can be a problem for elderly people because, along with the water, some of the blood's natural anticoagulants (including a substance called protein C) are shed by the kidney. This has the effect of making the blood more sticky and prone to clot, so heart attack risks increase in the winter time. This probably plays a small but significant role in the annual "excess mortality" (in other words a blip in the death rate where more people die than expected) associated with winter. In the UK the winter excess mortality is about 30,000 deaths. 12,000 of these are due to the flu.