Adding AC units to trains which travel through tunnels with minimal clearance is the achievement - Can't make the trains any bigger and there's no room in the old ones to just tuck an HVAC in without make them even more cramped.
Headroom is not an issue - there is plenty of room underneath the trains between the wheels. They then pump the cooled air up through the walls to where they want vents. Sometimes trains use the space between the wheels for passengers, but that has significant disadvantages and so should be avoided for subways (it is worth it for street running trams!),
