I uninstalled the game, turned off my tablet and put a new SD card - 64 GB Ultra speed, genuine one from Sandisk. Then I formatted SD as NTFS with default cluster size in Windows 10 (it was NTFS already, but I've decided to give it a quick formation because previously this card was installed in nVidia Shield), installed HoMM3 again, on D:, updated the game with the GOG patch. Alas, problem still here.
H2IWclassic: I would advise against jumping straight to a new OS so early in its release cycle, especially Windows - you'll come up against all of the usual early adopter problems, incompatibility being one. As the GOG disclaimer reads: "Please be advised that Windows 10 operating system will receive frequent hardware driver and software updates following its release; this may affect game compatibility " In other words they don't guarantee games will work perfectly at this stage.
I agree with your point, but being a notable digital distributor, surely GOG can't deviate from supporting the latest version of Microsoft OS for a long time. They'll have to embrace it, and better sooner than later :D. In this case, one should consider me as Windows 10 GOG tester. So far I've tried ~30 games from my modest GOG library on Windows 10, and noticed only 2 problematic games (HoMM3 and Settlers 3, single.exe of latter runs strictly in background) out of those thirty. Furthermore, I've noticed strange behaviour of Galaxy client on my tablet which I would like to report later.