What Marla has told you is the conventional wisdom. I have a mud pond - so you can't STOP feeding the fish all winter long. They suck on the mud and plants, and so long as the water is warm enough to motor about, they are eating.
They hunker down and don't move around a lot when its cold.
I think its ok to feed at cooler water temps - but only high fibre, low calorie things, like spinach, lettuce, peas...
Sort of what a fish would find in a mud pond.