If you are producing or selling nuts per these specifications, you need to buy the specs.  You can view brief descriptions and purchase ASTM standards at www.astm.org
The specifications are
A563-00 Standard Specification for Carbon and Alloy Steel Nuts,
F594-02 Standard Specification for Stainless Steel Nuts, and
F467-03 Standard Specification for Nonferrous Nuts for General Use,

Of these, I believe only certain grades of A563 nuts are plated. Also, as thread tolerances are involved, it is necessary to take any coating thickness into consideration when manufacturing the nut.  Plating or coating cannot be added ad hoc, it must be allowed for.
I don’t have these specifications myself, but a catalog shows that Grade DH is available in both plain and galvanized (hot-dipped or mechanically plated)* finishes.  Grade C is available in plain steel, and grades C3 and DH3 are weathering grade steel (not normally plated).
* Electroplating is not normally used for high-strength fasteners due to the danger of hydrogen embrittlement.  Of course, zinc coatings (galvanize) can be chromated for better corrosion resistance.

F594 nuts could be passivated per ASTM A967 or QQ-P-35C for improved corrosion resistance, but would not normally be plated (except perhaps on the threads with nickel or silver for galling resistance).

F467 nuts are of materials such as aluminum, chromium-nickel, copper (& brasses & bronzes), copper-nickel, and titanium alloys.  Some of these materials would have better corrosion resistance if plated with electroless nickel (e.g., per ASTM B733 or MIL-C-26074), but of course thread tolerance could be a problem.  Aluminum alloys can be chromated per ASTM B449 or MIL-C-5541E with negligible effect on thread tolerance.

This answer is based on my knowledge of the materials and metal finishing; you really need the ASTM specs to be sure of what is permitted.
Ken