full stop on the chemicals. been there. done that. regretted it.
I had my pond stocked with yellow perch - they dont mind cold or warm water.... the perch minnows eat mosquito larvae. But I had algae issues, and so I used chemicals.... i got rid of the algae..... and also killed the snails, frogs, water beetles... and all the fish. Bad Move!
What I then did is spend $40 at a pet-store, on a bunch of gold-fish and a bunch of feeder-fish which looked just like goldfish, but were smaller... probably the same thing... bu the feeder fish where dirt cheap. Like 50 or so total. Goldfish were 2"+/- long, and the feeder fish wee like 1".
I got a mixture of colors of fish just for fun. Orange, White, Grey... and a bunch of multi color ones.
Well.... they breed.... I have several thousand in there now. Biggest one is maybe 4" long?.... but only a few that size... most of them are 2-3" max, and schools of tiny minnows. They eat all the algae. I have had ZERO algae issues since I put them in. Pond Algae is a non-event for me now. Zero maintenance.
The fish will breed and eat as much as there is food. It's self regulating. I see no dead fish around... I see a blue heron come for lunch once in a while, but it doesn't stay long if our dog happens to be outside. I see a snapping turtle waddle over once in a while.
My pond freezes over from Dec to Apr., but because it's 6' deep, and about 1/4acre in size, and it doesnt freeze all the way to the bottom. So the fish stay low in late fall - in the water - and burrow into the mud and pretty much "hibernate". In the spring, out they come.
All the other frogs and critters get to live, because the fish don't eat them, and I dont use any chemicals any more. The tiny gold fish minnows, when they hatch - eat the mosquito larvae, but I sprinkle the pond with some BTI in the spring and that also helps. Bacillus thuringiensis israelensis.
The pond looks awesome - with the schools of fish roaming around... but it's not overrun.
Been this way for >10yrs now.
Not sure where you are, but even if your pond is shallow, as long as it doesn't freeze solid down to the mud, you'll have no issues with the fish freezing/dying over the winter.
Feeder fish look like this (stock photo - not my pond )