Only if you purchased InDesign through the Adobe Creative Cloud. Then you can install two copies of the applications on either Mac or Windows.
If you purchased a license for a Macintosh, you can't run it on Windows. To move to Windows, you have to procure and fill out a form (you can get it from Adobe Customer Service), uninstall the application from the Macintosh, and get a Windows version.
InDesing files are completly cross-platform except for some fonts. Older Mac format fonts cannot be used on Windows, but OpenType fonts are 100% cross platform compatible, and most Windows fonts can be used on Mac as well (though you may have to add them to InDesign's private fonts folder.
Sorry, I re-read your question. I thought you were talking about moving your licensed copy of InDesign from Macintosh to Windows. Time for another cup of coffee. ;-)
No problem at all – I really appreciate your help!!!