Ah, water management. Key with finding happiness with ducks.
I would give the ducks their own watering station.
It is best for them to be able to wash their heads frequently to avoid infections.
My approach is to place a straight-sided pot in the bottom of a large plastic dog crate. I put an inch or two of pelleted sawdust in the bottom of the crate. Ducks walk in, drink, dunk their heads, make some splash that is quickly absorbed by the sawdust, and walk out.
Keeps the bedding dry and the ducks healthy and happy. Their shelter stays above freezing.
For outdoor water, I empty ice and refill once or twice a day, and they have access to the above-freezing shelter throughout the day.
There are many ways to do it right, by the way. Try a search of the archives using the keywords water and winter.