For a pond to be effected by
'layers' in the winter it's probably going to need to be in the in the
region of about 100ft + deep. For a 3ft deep pond the water surface temp
will be the same as the bottom temp whether the pump is running or not.


No it won't. If it was, ice would form at the bottom of 3' deep ponds. As it
is ice is less dense than the water at the bottom of the pond (which is densest
at 4 degrees centigrade) and so forms on the surface of the water/pond.

Pumps should be turned off over winter, and ice which forms on the surface of a
pond should be melted to allow the escape of toxic gasses that can build up
over time. Breaking the ice using physical force can injure the fish in the
pond.

I hope that this clears a couple of points up.

Dave.