I don’t think mosquito larvae harm chickens.
I also don’t believe the barley dunks that kill the larvae harm chickens (I am less sure of that so worth doing research).
What I would do is just float a dunk in the container in the summer to get rid of them. Or cover the top with mosquito netting.
With those temperatures there won’t be any ice to break. My 5 gallon bucket with horizontal nipples doesn’t freeze until it is below 24F for the whole night.
It gets colder than that here in NJ and I stand the bucket on a very low wattage heat pad and that is plenty warm enough to keep water...