Dry skin around the eyelids can be very common in the winter time. The cold air dries the skin out but it does not have to be cold outside and causes flakiness around the eyes. You can try these below steps and know how to apply Vaseline on your eyelids:
First of all, get the skin back to look healthy and smooth just to remove the anything from the face care regime and it could be drying the skin out and make the issue worse. There are some makeup remover and can draw out moisture from the skin. This is generally more noticeable in some sensitive areas like the area round the eye. You can use a alcohol-free, gentle makeup remover to prepare the skin and do not ever forget to apply it directly in the eyes.
You can put a thin layer of Vaseline under the eyes and it will lock in moisture and it forms a protective layer. This layer will also stop cold weather and irritants from making this eyelid issue even worse.