What you are describing from a Mac perspective is how Spotlight on a Mac works. As Barney-15E said these tags (as used by Spotlight) are metadata and cannot be used by Windows since Spotlight is an Apple only feature. I don't believe they use resource forks but that is not really relevant.
There are two possibilities that may work between Mac and Windows.
Firstly Word itself has an option in Properties in which you define a series of keywords. Open the Word document, go to the File menu, select Properties, then click on the Summary tab at the top, and look for the Keywords box. Clearly this information will be stored in the individual Word file and is supported on both the Mac and the Windows PC. However how you could use that for searching I don't know.
The second possibility is that on a Mac with a Mac file server it is possible to have Spotlight indexing take place so that the client Macs can search files and tags on the server. Windows has a similar feature called Windows Search Service. It is possible to have a Windows File Server and install on it additional software called ExtremeZ-IP. (Now called Acronis Access Connect.) This software was originally just for adding Apple compatible File Sharing to a Windows server but it now also can use the Windows Search Service and convert the results to a form that a Mac client can use via Spotlight. Therefore in theory Windows PCs and Macs can both search the same files on the same server. See http://www.acronis.com/en-us/mobility/mac-windows-compatibility/