Does an MOT check air conditioning?
No, not in the way most drivers mean. An MOT does not check whether the air conditioning blows cold, whether the system needs regassing or whether the AC compressor works properly.
A car can normally pass an MOT with air conditioning that does not blow cold air, as long as other safety and visibility requirements are met.
The important exception is visibility. If the ventilation, heater blower or demister cannot clear the windscreen properly, the problem may become relevant because the MOT checks whether the driver has an adequate view of the road.