A quick google search on Zinc Sulfate yielded this interesting page.
Briefly, it's fairly innocuous in an of itself, but like many inorganic salts, too much can have environmental effects. If you have runoff into waterways, it's toxic to aquatic fauna. I don't know how much you have to use to control moss. Use according to label and you're probably okay.
From the website:
What happens to zinc sulfate in the environment? Zinc naturally occurs
in the environment. It can be found in animals, plants, and soil. Zinc
may come from natural sources, pesticides, or human activities such as
farming, and the production of batteries, animal feed, and metals.
Zinc is also used as a food additive.
Zinc sulfate is an inorganic salt that dissolves in water to form zinc
ions. The formation of zinc ions depends on water pH and the presence
of agents that can bind and capture zinc. Solubility makes zinc
available to plants and other organisms in soil; that availability
depends on soil pH. Zinc in the environment is considered immobile
because different substances bind to it.
Can zinc sulfate affect birds, fish, or other wildlife? Zinc salts are
slightly toxic or practically non-toxic to birds and highly toxic to
freshwater fish and invertebrates. No data were available on toxicity
to bees. Bees and other pollinators are not likely to be harmed
because they do not eat much plant material.