The circulating pump and small compressor would just slowly offload heat from the pond water and dump the 'free' heat in the house. It would not freeze the pond by itself, but when ambient temps are below freezing it would help remove that trapped heat from the water and from the ground to assist in getting 'safe ice'. Once the heat is out of the ground and the mass of water has chilled and we are making ice due to ambient conditions alone we would turn it off.
I think my heavy fall of oak leaves and the turf leading up to the pond is what insulates so well. Also since we had such a warm Dec I actually refilled the pond a few times with well water so I probably added a big 'heat sink' with 50 degree water added in. The small circulator and small refrigerator unit could help us.
But you are right, operating costs, the process of adding a closed loop 200' away would be pretty crazy...
Would be wiser to get a pond that doesn't leak so when the water cools in the fall I don't have to add any
