[DZEE'S LX]

Someone has simply bypassed the heater core. I can think of two reasons why this might have been done:

1. Heater core is leaking. You don't mention the year of your car but most fox body Mustangs are a PITA for replacing the core. You have to pull the console, instrument panel, and dash to get to the case that houses the core. This can be a significant and frustrating job, but it is definately doable if you have the patience for it.

2. Mixer door is not working right and someone wanted the air conditioner to run colder by having no warm air mixing when the A/C is on.

3. Someone told the previous owner that bypassing the heater core would produce an extra 50 h.p.

I'd guess reason #1 is the culprit but you can simply hook the hoses back up and see if anything leaks inside on the passenger side or under the car after running the engine at temp for awhile (possibly days). If your windows fog up easily that is also a sign of a bad heater core. You can also smell the antifreeze because the fan will fill the cabin with that lovely scent.

Can't remember which hose goes to which side.

Good luck!