Does Exposure To Cold Weather Cause Any Damage To Brain?

Dear Doctor,
I have a question regarding taking a shower then going out into cold weather. If I take a shower with warm water and then I go out when its pretty cold outside, without wearing a hat will I get sick? Someone said to me that the pores stay open after taking a shower, so if you go outside into cold weather the cold will pass through your brain and can cause damage. Is this true?

Thank you