The Moon would experience the seasons every ~27 days (depending on location and the lunar standstill every 9.8 years).
The logic for this argument is (assuming an atmosphere, i.e. widespread surface thermal transference and minimally discounting the intense semi-global storm systems):
During the ~10+ days of the cycle the Moon is closer to the Sun by ~240 thousand miles than the Earth, this almost completely eliminates axis tilt and inclination as a viable season indicator.
Due to tilt and inclination there is a portion that never receives Sunlight. This area can be equated to the polar regions on Earth, the the "atmosphere," if anything like Earth's, given the surface area (thermal mass) and reflectivity of the Moon's surface, a much more varied ground temperature versus air temperature than the equivalent polar regions on Earth.
The surface temperatures will most likely range from -160 degree F minimum (it will receive a lot of energy from Earth during the dark times + surface convection) to 200 degree F, with a very high probability of damaging wind storms Moon-wide constantly. Due to the small surface area and the thermal differences between the sunlit side and non-sunlit side.