Moisture/Frost on inside of exterior garage drywall

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We have a 1.5 attached garage that is drywalled. We do not know if there is insulation behind it or not as we purchased it about 6 months ago. There is some insulation in the ceiling. The house is 44 years old. There is no drain in the garage but it does have a small window. We cannot keep our vehicle in the garage if it is wet or covered with snow as the walls, service door and window will be covered with water/frost or ice depending on the outside temperature. The temperature inside the garage is usually above freezing. What can we do to solve this problem so that we don't have to leave our vehicle parked outside during the winter? We assume that having the drywall wet/frosted will ultimately cause damage. Do we insulate? Tear out the drywall? Add a floor drain? Please HELP!