iPod nanos will work with any (recent) version of iTunes. The current release (12.2) requires Windows 7 or later, but you should be able to install the immediately preceding version (12.1.2) - direct links to the installers as follows:
The third of these - which is actually the 32-bit application with a 64-bit installer - should be used if you get a warning about video card incompatibility when you install the standard 64-bit version, but also may resolve issues with playback, QuickTime compatibility, and problems with some third-party applications (including Outlook).
Unless you're anxious to make use of the new Apple Music service (which requires 12.2 but doesn't support the nano for offline playback) 12.1.2 is functionally equivalent and more stable.
You don't say which edition of Windows you are using, but you should note that:
- Windows XP is no longer supported by Microsoft - no security patches have been released for over a year and it is increasingly vulnerable to viruses and other malware
- Although Windows Vista is still supported, that will end in less than two years' time. Also, there is a long-standing issue regarding compatibility of iTunes with Vista - it installs and runs OK, but generates errors on exit.
In either case you should investigate updating your computer to a more recent edition of Windows, or replacing it with one running Windows 8.1 or (within the next few days) Windows 10.