There are a couple distinct possibilities here.
If you find that the skin of your hands turns red and stays red for days or weeks during cold weather, then this probably represents a type of skin dryness or eczema
. This is very common in cold weather, as the cold tends to worsen dryness and inflammation of the skin. Other symptoms might include burning or itching of the skin. If you think this is what is going on, then it is important to protect the hands from over-washing and harsh soaps. It is also important to apply a good skin moisturizer on a regular basis. You may also need a topical steroid cream to reduce the redness, but your doctor
can help you decide this.
If on the other hand, the change in color only occurs when you are exposed to cold temperatures but then improves when your hands warm back up again, this might be something called Raynaud's phenomenon, which is a condition in which the blood vessels are sensitive to cold temperatures and constrict too much in response to exposure.
Both possibilities need to be investigated and confirmed by a doctor, so make an appointment with your primary care doctor
at your convenience.