any type of carp will survive but the cold winters will cause issues unless the tank is partial underground. Better yet put in a Plecostomas, a type of catfish that you can get at almost any pet store but again the winters will kill them. A $5 fish for once a year isn't bad. We recommend putting these guys in Koi ponds to help reduce the growth of algae.

Koi will produce more waste, which will need to be either filtered or will break down in the tank and feed the algae. Do you really want the fish, or are you trying to solve the algae problem exclusively? Shading out the algae may be better, or using plants/moss to consume any nutrients in the water. Would cows drink from a tented tank? I haven't had my koi extremely long, but I really struggle to imagine them getting used to large thirsty cows on a regular basis.

Could you possibly instead plant out water lillies in containers in the center of the pond, so the cows can drink around them, but the majority of the tank is shaded?

Koi are much too large for a 350 gal tank, and the water being fertilized by fish (poop) will create more algae not less. If the water is turning over regularly (several times per day) is the algae really that severe that it cant just be cleaned out periodically? Is this string algae we're talking about? What organic material is getting in there that the algae is able to grow - is it leaves and stuff? If you just remove the organic debris and scrub down the sides periodically I think youd have very little nutrients for algae to grow.