Everything I tested
What does not
I do not know of anything that is not working
What was not tested
I have installed Heroes III yesterday on slackware 12 on a dell inspiron 1501 using the ATI video driver, with the two expansion packs, and it works. Interesting thing is that I have cracked the exe file because I was bored to always insert the cd on an old computer of mine using XP. Copying this cracked version to my new (current) computer without install was working in XP, but not in wine, wine complained about missing files. So what I did was that I have installed the original version (no expansions), and it started ok, then I just deleted the files and copied the cracked version with the expansion packs into the location of the installed version, and it is working great. Admin's explanation: The installer creates registry keys which are necessary to play the game.
|Ubuntu 13.10 "Saucy" i386 (+ variants like Kubuntu)
|Dec 30 2013
|Ubuntu 12.04 "Precise" amd64 (+ variants like Kubuntu)
|Mar 05 2013
|an anonymous user
|Oct 18 2010
|Ubuntu 9.04 "Jaunty" i386 (+ variants like Kubuntu)
|Dec 05 2009
|an anonymous user
|Debian GNU/Linux Unstable "Sid" x86_64
|Jun 13 2009
To get multiplayer working, you need native directplay dlls. The old howto had a link pointing to outdated directplay dlls which cause problems with wine and generally don't work as expected. However with the latest dplay from DirectX 9.0c multiplayer is (almost - see note for details) flawless.
In the wine wiki is described how to get native direct play dlls.
Personally I would recommend using winetricks directplay which installs dplay dlls and sets overwrite in winecfg, however you may choose do install manually those files in which case you need to:
You can now play Heroes 3 in HD, utilizing the full size of your screen, thanks to Heroes3HD mod. It doesn't change anything gameplay wise.
With recent Wine releases, Wine prefixes are set to Windows 7. Currently, it causes rendering issues when HD or HD+ mod are installed.
winecfg and setting the Windows version to Windows XP solves the rendering issues.