I need to weld some nuts to a steel tube. Are there any issues with using regular zinc coated nuts or are there other, plain steel nuts I should be using?
They should weld just fine. If you are using a mig you may want to grind some of the coating off where you are welding if you get and holes in your weld. Keep it ventilated well, zinc smoke will fuck you up.
I do this a lot at work. It's not easy to weld galved steel, so either grind/sand off the zinc on the nut (not the easiest to do if they're small!) or use a plain steel nut. If the tube is galved, sand the galv off that too around the area of the weld.
The fumes from zinc are toxic so wear a mask and weld in a well ventilated area.