"High-dynamic-range content doesn’t automatically display in HDR. It plays in standard dynamic range by default. You need to head into Windows 10’s display settings and activate HDR to enjoy the enhanced visuals, but doing so plunges all non-HDR content into murkiness, casting a dim, gray hue over everything else. It’s ugly and unusable for standard tasks, so you’re forced to head into the display settings to manually enable HDR whenever you want to watch a video or play a game, then disable it when you’re done. FreeSync 2 displays include technology to automatically switch to HDR when you boot compatible games, then switch back to standard desktop settings when you’re done, but overall, the HDR experience on Windows 10 is a wonky, bleeding-edge mess."
So I'd say you likely are forced to keep it on in W10 and change as needed currently. I don't know if you'd need a new MONITOR or whether they can switch in software with a driver update (NVidia or AMD) for your existing Freesync 1 or GSync monitor.
I don't have an HDR screen and this is the best info I could find.
*I'd also say see what happens to HDR support in a game if you disable it for W10. Is it greyed out now? If so I guess you are SOL currently.
It's also likely Microsoft will fix the visual issues. I know it's already improved for the desktop so hopefully that will continue.