Nope they lay when they want. My females never lay over winter. I guess you could try adding light but I have never done this so not sure if it would work for ducks.
I couldn't imagine hatching ducklings through the winter here in MI. They'd have to be raised in a brooder, as it's too cold here and 'scovies don't brood their ducklings like other ducks do... I don't know how I'd keep 'em warm or keep their water from freezing!
I also HATE brooding ducklings artificially and I bet I'd hate it worse in winter. You're braver than I to WANT to do that!
Mine don't lay in the winter. They START occasionally as early as Februrary here. But, it's kinda a piddly lay, off and on. Since the eggs freeze I just take 'em away. They tend to stop again until April, and start accumulating eggs then.
My Muscovys usually has a month break once her ducklings stray from her. They usually do that to her when they are about 2-3 months old. Then shes laying again. One of my girls is laying right now. 7 eggs in an old dog house... she will continue until she gets at least 22. [thats usually how many she lays, although i got 25 from her in July.] I let her do the setting, but since im from orange county, california... our winter weather isnt that bad... but if your from the north, id say collect them and incubate them yourself or use them in cooking! I love Muscovy eggs in cake batter. [i dont know why?]