This is a common question that I get and both have their place. Let me explain:
Warm Compresses: Warm compresses are the mainstay of treatment for any eyelid issues or dry eye related to the eyelids. For example: styes, swollen red eyelids, or excessive watering of the eyes is a result of the glands in the eyelid becoming plugged. Warm compresses help open up the glands and return your eyelids back to normal.
Cold Compresses: If you suffer from allergies or your eyes itch, you want to do cold compresses. The cold will constrict the blood vessels and reduce the histamine brought by mast cells that travel in your blood vessels. Histamine is what causes your eyes to itch and limiting that will reduce inflammation and some of your symptoms.
In both cases, you may still need a prescription eye drop or antibiotic to get you back to 100%. However, using this as a guide, you can get a head start before coming into the office!