I have always found that I get sick, quickly from breathing zinc oxide fumes. Very quickly. One whiff is enough to just about make me puke. It's a mild poisioning! I get similar reactions when working with certain sprays like MCPA Amine 500 and to some extent 2-4D.
I don't take chances with zinc anymore. If I have to weld galvanized metal I grind or wire wheel the coating off as best I can and weld at arms length in a cross wind.
Granted some may be less sensitive than I am, it's still going to get you eventually if you breath enough of it.