According to leading Eye Doctors it is possible for your eyes to get burned by the sun so better be careful.
Even when wearing contact lenses with UV protection, the strong sun especially in gulf countries of the Middle East such as the United Arab Emirates, Saudi Arabia, Kuwait, Qatar and Bahrain can burn the areas of the eye which are not covered by the contact lenses.
This is why it is so important to wear sunglasses which protect against UVA and UVB rays. Sunburn is distinctly different if it occurs on the skin or to the eye. While the effect of sunburn to the skin are relatively immediate with redness, pain and eventual skin peeling, sunburn to the eye occurs over an extended period of time and can lead to a thickened tissue within the eye. By then it might be already too late for the eye to heal naturally and it would require surgical treatment.