A lot of conditions associated with the under-eye area is genetically determined.The skin here is very thin, so it is not recommended that you apply any cream/lotion here.
Any excessive manipulation will cause wrinkling of the skin.
Your skin is being sensitive to the changes in temperature, that is why the color changes.
You can apply sunblocks in summer to maintain even skin tone by preventing tanning of face.Similarly in winter keep skin well moisturized to prevent excessive dryness and color changes.
I have the same problem and it is associated with my diagnosed Adrenal fatigue and Hypothyroid. To boost my adrenals I have to take extra B-vitamin supplements and eating plenty of raw fruits and veggies every day has helped. The biggest help I've seen though is from getting enough rest and trying to keep stress levels down, as well as taking Sole (a solution of Himalayan Crystal Salt and Water).
is it vitamin b12 that i need