The first step in deciding whether to use existing heating ductwork for a new air conditioning system is to determine the location and size of your ducts. You must make sure they are the right size to handle the output from the cooling unit, based on the air flow from the unit. Normally an effective distribution system for heating suffices for cooling, but some situations require changes.
A second consideration in adding air conditioning to an existing heating ductwork system is the location of the input. Combined heating/cooling units have a single entry and return point. Adding air conditioning may require a second entry and return point. Ideally, these are located close together; putting an air conditioner on the opposite side of the house from a furnace may require additional ducting.
Air conditioning ducts must be balanced, just as heating ducts are. That means a return system must take "used" air from the house back through the unit. Outlet or supply vents are located on outside walls, usually near windows; return entries usually are in a hallway or some other central location where air flows naturally. The return system must be able to return all of the air being put into the duct system by the unit.
Special attention should be paid to areas that need more cooling than heating. Sun rooms, for instance, with lots of glass and sun exposure, have different heating and cooling requirements in different parts of the country. This requires complex ductwork adjustments, and probably professional assistance.