It's hard to know without trying it. I deployed an FMRuntime from v6 about ten years ago that kept working for many users until Vista.
The FMI links Wim gave also show that FM10 has issues with Windows 7, but some users of an FMRuntime v10 have not encountered those problems, possibly because of the specific features used by some runtimes.
It really depends on your runtime and why/how there may be problems. Often it is specific featues/script steps which cause failure.
However, Wim is correct in that you certainly can't assume older FM versions will keep working after an OS upgrade.
I am currently using Windows Hate, so provide a link and I will let you know if works. I am using Pro12 advanced which seems to work fine.