I think the main problem with winter cats is location. You have to be in a deep area that holds a lot of wintering cats. In fisherman says jigging outproduces tip ups for them, but you need a long pause.
I fish for winter cats in the upper Colorado near Grand Junction Colorado. It has a flow a little bit greater than the Connecticut and is deeper but also narrower. The cats seem to concentrate in 40 - 70 foot plus holes, which are pretty numerous in the canyon areas near the Utah border. They appear as a big dark area on sonar, and will use all depths.
Not many of the fish are active, but the sheer numbers of cats around can make fishing good. Cats don't hibernate in the winter but they concentrate in wintering holes, so if you are fishing the wrong hole your SOL.
That surprises me grumpymoe that more wouldn't be caught in the Red River. My guess would be that they would concentrate in the deeper portion of the river near the lockport dam, and I would think maybe that part wouldn't freeze or would be unsafe do to so much current, but I have never been there so I can't say, that's only a guess. Doesn't the red get wider, shallower, and more lakelike closer to the winnipeg?