Posted September 04, 2017
The most recent updates for the Heroes III HD mod now include an in-built multiplayer lobby for the Horn of the Abyss mod. It's in beta and is therefore a bit rough around the edges and has a few features missing, but the core stuff like rooms, chat and connection work. Don't know when/if the unmodded game will be supported, though.
https://sites.google.com/site/heroes3hd/eng/download
https://sites.google.com/site/heroes3hd/eng/download