Apparently, there was not any air conditioning when George Washington was living there. However, he was smart to have this cupola in the middle of the house above the roof. When those windows are open, the hot air inside the house will funnel through it providing good ventilation to cool down the whole house.
The back side of the mansion has some big area with chairs for visitors to sit and enjoy the view.
The back of the house is facing the Potomac River, very beautiful.