EDIT: ***SOLVED***
The cursor doesn't work during the opening intro the first time you install the game, and you have to wait through the whole intro in order to get to the game with working cursor.

...

Hello and thanks in advance for any assistance!

I purchased HoMM3 from Gog a while ago.. it worked OK on previous Ubuntu versions but now doesn't work after updating Ubuntu to 16.10 (from ~14). The problem is when I launch HoMM (via Playonlinux) the window doesn't maximize and moreover the window doesn't recognize the cursor. I can still use the cursor in the background on the desktop and other simultaneous applications, but when I move the cursor over the HoMM window it disappears from view, clicking anywhere when it's disappeared over the window traps it in the window, and moreover the click is never registered in the game so I can't get beyond the credits. I can only retrieve my cursor to close the game by pressing the windows keyboard button (which in Ubuntu brings up the search).

For reference, I used the following instructions to install the game:
I'm not allowed to post the link, suffice it to say that it's a guide from gamers on linux website and it seems reputable.

I didn't install the HoMM3 update because as I understand it the update has now been included in the main gog HoMM3 file, and anyways the update doesn't address the aforementioned issue.

Solutions that I tried and that failed:

- Searching the web for several hours
- Adjusting Playonlinux 'Display' tab options
- Adjusting Wine configuration 'Graphics' tab options in PLayonlinux (unchecking the 'emulating a virtual desktop' option makes it fullscreen but with no cursor nor any X button to close the window I must restart the computer)
- Trying different Windows versions in Wine, as well as different Wine versions

Running Playonlinux's debugger yields the following:

[07/20/17 15:58:51] - Running wine-1.7.55 Heroes3.exe (Working directory : /home/andrew/.PlayOnLinux/wineprefix/Heroes3/drive_c/GOG Games/HoMM 3 Complete)
err:winedevice:ServiceMain driver L"WineBus" failed to load
fixme:win:EnumDisplayDevicesW ((null),0,0x33f698,0x00000000), stub!
fixme:x11drv:X11DRV_desktop_SetCurrentMode Cannot change screen BPP from 32 to 16
fixme:x11drv:X11DRV_desktop_SetCurrentMode Cannot change screen BPP from 32 to 16
err:ole:CoGetClassObject class {5959df60-2911-11d1-b049-0020af30269a} not registered
err:ole:CoGetClassObject no class object {5959df60-2911-11d1-b049-0020af30269a} could be created for context 0x1
fixme:dplay:IDirectPlayLobby3AImpl_RegisterApplication :stub

Likely insignificant but possibly significant points:

- When I run HoMM3 the window has an X and a minimize button but no maximize button and I obviously can't adjust the window size by clicking and dragging the sides
- The installation guide says to use Wine version 1.7.6 but that version isn't available so I used the next closest. It also says to install libraries but I was unable to do so due to a glitch, but it explains the libraries are for things I don't need such as multiplayer functionality.
- The guide also says: "On the wine selection window, select 1.7.6 and click next. Make sure you select '32-bits window installation' if you are on a 64-bit system." ...selecting 32-bits for 64-bit system, I guess, is right, unless the guide is wrong..
- Upgrading to HoMM3 WoG afterwards seems like such a far away impossible dream :(

Please any help is direly needed! I searched every single Google result for "Playonlinux" + "homm3" + "cursor" and there wasn't a single mention of this problem. This is one of only two games that I ever play, so thanks for your help I really appreciate it!!

HoMM3 is definitely usable under Wine. My settings, some of which may be relevant and some of which may not:

Wine version 1.7.55
Wine Windows version: Windows 98
Library overrides: None.
Graphics:
* Capture in fullscreen: NO
* Allow window manager to decorate: YES
* Allow window manager to control: YES
* Emulate virtual desktop: YES: 1280x1024
Audio: (System default) for all; my speakers produce sound at the right times
Drives: only C:

I always run HoMM3 under a taskset to a single CPU, due to claims on the forum that it is unstable on multicore systems (which is pretty much everything these days): /usr/bin/taskset -c 1 /usr/bin/wine Heroes3.exe; I never personally experienced those crashes even before the taskset, so I cannot say whether this step is required.

The only issue I have noticed is that sometimes the graphical output will become confused and hang. Pressing F4 to unsuccessfully switch to fullscreen mode recovers it (and produces a message box which must be dismissed).

Yeah, I know HoMM is usable with Wine, I had it working before like I said. I'll keep that taskset thing in mind since I did routinely get glitches before, though.

If nobody here knows the answer, perhaps could you direct me towards what community to ask next? Does it appear to be more of a Playonlinux problem, Wine problem or Ubuntu problem?

Yes, you had it working before in an old version. I have it working (just verified) in exactly the same Wine version as now fails for you. It worked for me without any particular configuration changes. I do not use Playonlinux. I used Wine to run the GOG installer, ran Winecfg to set the options I described above, then ran Wine directly on the game. That suggests the Wine version is not the issue, although Wine options could be. Have you tried it in a clean Wine prefix? Have you tried not using Playonlinux?

I'm pleased to say that I discovered the problem, alas the cursor doesn't work during the opening intro the first time you install the game, and you have to wait through the whole intro in order to get to the game.

You can't skip the intro in Windows the first time you tun the game either. After that a registry key will be set. That was intentional.