I am not sure the water freezing will do it...My water is frozen every morning, and I won't lie, I have been known to take my sweet time getting up to the coop to being them new water, but haven't missed an egg beat so far from it..then again we are talking about the water freezing around 3 or 4 am and me refilling it at 10 or 11 am...We also ran out of food for a few days, I noticed the chickens just foraged way more for a few days...I just got them a new bag of food today and not one has come to see me or check out the yard...I think I am going to take their feeders away in the summer and just give them handfuls of food a few times throughout the day. That was what I started doing as the food got low and that got them up and moving and being chickens. If given a full feeder they are a bunch of lazy layabouts...I can say that the eggs are smaller when they are foraging and only getting a few handfuls of food everyday...but I still get the same number of eggs, just slightly smaller than when the feeder is full...I also noticed a size difference between giving laying pellets with 16% protein, and chick starter with 20% protein...the eggs were a size larger when the hens were eating all the chicks food...
I can't wait until full on spring time, with warm weather and bugs and all that.