Yes, the herpes viruses (such as herpes simplex and herpes zoster/chickenpox) viruses can occur in the eyes.
Almost any part of the eye can be affected, including the eyelids, cornea, conjunctiva, sclera, and very rarely, the retina.
The symptoms experienced depend very much on which part of the eye is affected. Even then, there could be several forms of the disease in the affected part of the eye.
For example, there could be little blisters on the eyelid skin, or if the cornea is affected there could be eye redness, irritation, blurring of vision, etc.
The symptoms are not specific - ie there are other conditions that could cause the same or similar symptoms.
As such, it is important as always to consult a doctor in the event of such symptoms, so that an accurate diagnosis can be made and the appropriate treatment given.