Aftermarket air conditioning was available at least as far back as the 1953 model year. I have a Desoto TV commercial where the Chrysler Airtemp system is demonstrated (it takes up the whole back shelf of the trunk). Kaiser-Frazer's "air conditioning" was like that of the Nash Weather Eye system where air went through a venturi passage in the air duct; the air flow sped up, the temperature dropped a bit and moisture condensed and dropped out of the passage. The system was referred to as air conditioner in factory literature but it was in fact "conditioned air" as my uncle who was with Nash and AMC referred to their system.
A Mark IV unit could have been installed by a dealer but it was not factory unless there is a SPEC-FO number properly sequenced on the larger firewall tag. Check KFOCI HANDBOOK information on K-F cars for more information.
If you joined the club you should have received 4.0 when you joined; if you did not, 5.0 will go into distribution in the next few months (between October and the end of 2013).