meffcio: The mouse pointer in my installation of HoMM is pretty much just a box that inverts the colours of whatever's underneath. Unfortunately I can't attach a screenshot because I can't make on in game - none of the options work.
I found the solution :
1. Go to HOMM installation folder ( you can find it in GOG by clicking "more" and then manage your installation )
2. find file "Heroes.exe" and go to properties
3. set compatibility to windows xp service pack 3 and check "disable fullscreen optimization" , see the attached image.
4. run game and pointer will be there again.
Other solution but not prefered by me is to find file : dxcfg.exe
then change Scaling method from "Screen fit" to "Integer"