I would recommend that you go to see your primary care doctor
about this issue as soon as possible. They should be able to help you figure out what is going on.
Especially in winter months, once of the most common causes of red palms is eczema
or excessive skin dryness. In addition to a red discoloration, there are usually other symptoms as well, such as itching or burning of the skin, together with, sometimes, cracking, flaking, or peeling of the outer layer of the skin. If you have these symptoms, then they should resolve with the regular use of a good skin moisturizer. However more persistent cases may require prescription steroid creams, something that your doctor can help you decide about.
This could also, potentially, be a circulatory problem, such as something called Raynaud's phenomenon. In this condition, what happens is that the hands when exposed to cold air initially become very white or bluish in color and then turn bright red as blood rushes into the hands.
Finally, in a few rare cases, bright red palms may be a sign of a more serious underlying medical problem, such as trouble with the liver.
Go see your doctor at your earliest convenience!