We've lived with two different ponds, each for ten to fifteen years or so...they were old, probably built forty to fifty years ago. Both had no fish and no mosquitoes. They both had a healthy frog population and huge amounts of
dragon flies (whose larva, I understand, eat mosquito larva). The second pond also had snapping turtles and some kind of reed on one edge. It went completely dry only once in the fifteen years we were there and came back just as mosquito free. The year we moved away, lily pads showed up and no one has a clue how they ended up there. The first pond had herons visit frequently.
We never got around to doing anything with either pond, always low on our priorities, so I can't say how to end up mosquito free...it wasn't anything we did
I think if ponds are allowed to develop their own ecosystem naturally this is where one would end up though.
Neither pond was ever used by livestock that I know of.
I remember carefully looking for mosquito larva at each pond and being surprised that there was none.....
EDIT...and as Mary says in the post below,
BATS and BIRDS! We've always had a healthy bat population and a variety of birds. I think both might be as important as everything else.