I've heard both ways
I painted my galvanized pond, since I wasn't sure. After 5 years the fish began dying.
The paint was chipping off the pond, I think the goldfish were ingesting paint with the algae. I decided they were dying from the paint. I broke down the pond, fitted it with an EPDM liner and refilled and restocked, and the fish began dying.
I finally realized that they were eating flake food that was 10 years old.
If you can find a black Rubbermade stock tank, you can skip this question entirely.
Meanwhile, I've had people tell me that the galvanizing is not a problem.
I did see the tank that was painted rust eventually on the rim. If looks are important, I'd suggest lining with the EPDM from the start. An 8'x10' piece from JustLiners.com, cut a circle and one long rectangle, then fit and glue with the stuff they sell. I used the tube of sealant, the tape might be prettier as it tends to curl at the seams the way I did it.
The pond that I've installed at the elementary school science garden has no liner or paint, I figure that it will be discarded in 5 or 10 years and replaced.