To keep the answer short, Yes it does. Solar is only able to work if light is able to hit the solar cells that are beneath the protective glass that lays on top of it. The cleaner this glass is, the better the panels will perform which will increase your production.
No amount of rain will replace a proper cleaning. Do you only rely on washing your car with only the rain?
Studies from across the world have suggested different cleaning frequency depending on the area. In coastal and rural areas it is suggested for at least once every 6 months. Urban areas should be cleaned every 6-8 months.
In utah, it is wise to clean 2 times a year to protect the panels and keep efficiency up due to the polution and dust that floats in the air. The longer the dirt is on the panels, the harder it is to clean them.
Solar panels are made with tempered glass and solar cells, you don't want to clean the glass in extreme conditions. Having scorching hot panels and cold water will create cracks and break the panels.
The best way to clean is during the fall and springs months when conditions are suitable for both the panels and the safety of the cleaner.
cleaning in the winter is acceptable but not ideal.