That basically what I've done with my pond, except the water goes inside to my pump/filter room. Right now my pond is completely frozen over but the water circulates out of the pond through the bottom drain and into a settling tank in the filter room, then through a submerged filter in the settling tank and back to the pond again. Because the settling tank doesn't freeze over it effectively becomes the hole in the ice for allowing oxygen back into the water and undesirable gasses to escape. I have a small space heater in that room but generally only have it set on the lowest setting unless I plan to go in there for an extended period of time in which case I sometimes turn it up. Because the room is insulated so well and not very big it only takes a few minutes for that heater to heat it up to 80 F (26 C) in there.
I've done the calculations and if I decided to let that space heater run full blast all the time it would cost me about $30 a month. The only problem I have with humidity in there is with the warm air leaking past the metal door it tends to condense and freeze around the door jamb when it's very cold out and has a tendency to freeze the door shut. Not much of a problem though because once it warms up again the ice melts and the door opens freely again. In a pinch if I really need to get in there I can use a hair dryer to free the door.
This video shows the pond is still open a bit, but it has since frozen over completely and the ice is about 6" thick.