The color of your eyes should not effect how you see. Eye color is a result of pigments and some structural coloration from how a part of your iris is structured and reflects light. People with blue eyes are known to be more sensitive to bright light than people with darker eyes because they their eyes have less pigment to reflect or block the light from the retina.

Ordinarily no, except in one extreme case (see below): the color of your eyes is the color of the iris, which is a muscle that determines the size of your pupil. You only see light that goes into your pupil, so any light that hits and reflects off of or gets absorbed by your iris is light that you don't see anyway. So, the short answer is no.

That said, the pigment that colors eyes absorbs ultraviolet, so if you are repeatedly exposed to high intensity light, and your eyes are light-colored, you may damage your eyes. This is why people in the tropics generally have brown eyes, while people in temperate regions can get away with having blue eyes. Hazel obviously is somewhere in-between brown and blue.