(All tested on Windows 10 x64)

Windows/Intel display drivers moving all your open windows from your secondary display
 connected via HDMI to the main display the moment the secondary display is powered off
 (can not be fixed, afaik)

Windows losing window placements and icons when the secondary display connected via
  HDMI is powered off and back on again.
  (can be worked around)

For the latter there are two tools available:
 'Restore Windows' saves and restores window placements
 'Persistent Windows' saves and restores icons and window placements
  (did not work very well for me, but might work for you, and Windows 10 does automatically
   restore icon positions on secondary monitors, sometimes)

Run 'RestoreWindows.exe', it'll be in the background showing no information.

Once you switch off your secondary monitor connected via HDMI Windows will flip all open
 windows from the secondary monitor to the main screen.
However, thanks to that tool, once you switch on your secondary monitor again it will move
 the windows in question back to the secondary monitor from the main screen.
That's basically all it does.