Using a Adobe Zapf Dingbats character in Windows 2000 shows up as a Wingdings character on the screen, on paper, or in a PDF, or any combination. I'm not sure if this affects NT, but it is not a problem with Windows 9x.
There is a specific bug in in the Windows 2000 operating system (although Microsoft would probably tell you it's a feature) regarding font enumeration, where, when you choose certain fonts, Microsoft remaps what you asked for into what they think you want. Specifically with Zapf Dingbats, Microsoft, in a sense, says, "the user asked for Zapf Dingbats, but I'm sure the user really wants Wingdings, so I will use that instead."
This solution works with the AdobePS driver that uses PPDs to install printers -- I don't use the Microsoft-supplied version (using the Add Printer Wizard) so I can't comment on that.
If you open a printer's PPD file as text, you will find a list of fonts at or near the bottom of the file. The printer driver looks at this list and tells the operating system that these fonts are resident on the printer, therefore they do not need to be downloaded. In almost any PostScript printer, Zapf Dingbats will be in that list. What I did was just comment out the Zapf Dingbats line (which forces the operating system to think the font needs to be downloaded), then remove and reinstall the printer using the new PPD. To comment a line, place a percent sign after the asterisk at the front of the line:
Before: * Font ZapfDingbats: Special "(002.000)" Special ROM
After: *% Font ZapfDingbats: Special "(002.000)" Special ROM
The fix works for both physical printers and virtual printers such as Distiller.