We have just replaced the cabin roof airduct in our 1977 Piper Archer II
PA28-181.
The duct feeds fresh air from the rear mounted blower to each of the 4
overhead air outlets.
The air is controlled by a push & pull cable mounted in the duct.
With the air duct closed, no air being fed to the overhead ducts, there is
howling cold airflow up through the right side of the rear seat floor duct.

Having spent a goodly amount of time working on (and replacing) that
very same fresh air flapper (the one that controls the ceiling ducts)
in my '74 Pathfinder, I can tell you without hesitation that it has
NOTHING to do with the air coming in the floor ducts.

If air is coming out of a floor duct, you've got a bad flapper valve in
that duct. Make sure to check that the cold air isn't actually coming
from under the back SEAT.

If you have the bench seat, this is an extremely common place for air
to leak into a Cherokee. Luckily, it can be easily remedied with a
strip of strategically-placed closed-pore foam insullation, laid down
where the bench seat meets the bottom of the airframe.

This 75-cent piece of foam can make all the difference in the world.

The cold air flow with the overhead duct closed must be coming from central
air outlet under the belly of the bird ?

Nope. However, there IS an inlet on the belly that could be the source
of air leaking under the seat. This inlet on the bottom of the plane
is simply an open hole -- there is no control.

Our maintenance crew have had both the overhead duct system apart and the
rear seat board out to inspect that area.
Everything looks normal and they are perplexed how to cure the problem.
I wonder how many other PA28 owners with overhead fresh air ducts have had
this issue ?

I spent a dozen or more hours weather-sealing my old '75 Warrior. It
was colder than hell in the winter, and my poor kids had to fly wrapped
in a sleeping bag in winter. After methodically sealing the door, and
each leak (Example: Stuff "Nerf" balls in the floor ducts to really
seal out any leaking air), we could fly that plane in shirtsleeves, no
matter what the weather.

Good luck!
--
Jay Honeck
Iowa City, IA
Pathfinder N56993
www.AlexisParkInn.com
"Your Aviation Destination"