I'm new here and don't know if this will help (at least you'll know that it's possible), but FYI, I installed node and npm on Windows 10 and it works ok:
Microsoft Windows [Version 10.0.10586]
(c) 2015 Microsoft Corporation. All rights reserved.
C:\Users\xxxxxx>npm -v
3.10.3
C:\Users\xxxxxx>node -v
v6.6.0
C:\Users\xxxxxx>where node
C:\Program Files\nodejs\node.exe
C:\Users\xxxxxx>where npm
C:\Program Files\nodejs\npm
C:\Program Files\nodejs\npm.cmd