I do not have Ice over down here. That being said my 3AC pond is maintained at full pull with a lot of clear well water. I use pond dye thru late fall and winter to prevent algae and weed problems at depths during the really clear cooler weather months. The dye acts as a chemical shade by reflecting some of the blue wavelengths of light needed by the plants for photosynthesis. The plants cannot grow effectively without active photosynthesis. Dyes only inhibit plant growth below 18 inches of the pond surface. Color intensity must be maintained in order to remain effective at 18". Less color the deeper the sunlight will penetrate. It has been my experience here that from full dye @ 18" to not noticeable dye take about 8 weeks. I normally stop adding dye in Feb. so that the spring algae bloom I want will not be inhibited. The waters start to warm pretty good in mid march here.
As a side note I seem to feel that Dye tends to make the water temps a few degrees warmer in the upper layer since it catches a lot of the sun light. I would not be surprised if you find ice over to be slower, thinner and end earlier with the use of pond dye.
Oh yea the darker waters seem to help make it harder for unwanted predators to do their thing. wink