http://bugs.winehq.org/show_bug.cgi?id=3930
--- Comment #59 from Michał Z. Gołębiowski m.goleb@gmail.com --- FWIW, HoMM is also available on DOS and works way more reliable there. For anyone really wanting to play the game - you can buy it on gog.com, works perfectly for me!
This is quite common - win9x games are way more hacky than newer ones so it may be much harder to make them work in Wine etc. On the other hand, win9x games often have a DOS version that is eqsy to run on DOSBox (this is what gog.com uses, with proper presets).
This means that even without resolving this bug you can run HoMM with sound.