Yes, a cloudy day your eyes can be sunburned. Dry eyes are caused by excessive UV-A and UV-B rays. Not only the sun contributes to the sunburned eyes, but also the UV radiation which reflects off snow and water can cause sunburned eyes as well. felt a few hours later. So if you feel your eyes dryness, itchiness, burning, tearing and heightened sensitivity after sunburn, you should go to see a doctor because high visible or blue light can contribute to a marcular degeneration and lead to blindness at worst. So in order to protect your eyes from harmful rays, you should wear sunglasses whenever outdorrs and look for the words 100% UVA and UVB protection and HEV,near-UV,or blue-light filtering.