Are you running it through DOSBox?

How would I do that? I can't seem to figure out how to use DOSBox

EDIT: So far I can get it to open, but it crashes immediately. It only finally opened once I put my Windows 95 disc in and I set compatibility mode to Windows 95 on the editor. Just can't get it past the initial white screen when it starts.

If you install the DOS version of the game, the setup program should also install the editor, with a shortcut using DOSBox.

Anyway, HoMM 1 is hardly worth bothering with, when HoMM 2 and 3 are available.

I can confirm that in the installed directory there is only a shortcut to launch the game. There is no shortcut for map editor. Therefore some manipulations with DOSbox are required to launch editor. Can someone tell how to do that? This should not be an argument at GOG. Here every game has a value to somebody.

Having the same issue. Came across your post researching a solution today. Did you ever figure it out? From what I can see it appears to be a configuration change (?) that GOG may have done due to a specific Windows update(s). The Map Editor when launched from the HOMM directory says the Wing32.dll file is required. Adding the Wing32.dll back to the directory and/or Windows directory as Microsoft suggests doesn't fix the issue either. If you put the Wing32.dll in the GOG/HOMM directory, Windows doesn't like it and if you put in back in Windows, it try's to run the map editor, but asks for the original Windows 95 game CD.

Haven't played this game in over a year, but I used to be able to edit /launch custom maps when I originally download this game form GOG. I put in a queue with Support in hopes of maybe fixing the problem. I did uninstall the game, reinstall, and allow GOG to update the game and it didn't resolve the issue. I did notice that the DOS box menu options no longer has the map editor option it used to have. You only get 3 options to choose from now.

The map editor feature is still available if you happen to have Heroes of Might & Magic: Gold edition, which I believe combines the original game with the second game. Tried it out a bit and it is working for this version of the game.

No, its opposite to what you say. There is almost NO proper GOG releases for such old games. All ScummVM are broken
Most of DosBox are outdatet and DOS-only ripped. While heors1 game is originally DOS only, still Win-edition been superior and more updated. You need Windows version.
And it probably inluded in image disc present in game files... homm1.gog (copy and rename it to .img)
It should be multi-tracks but looks like there is no cue file for that bin. Bin itself (renamed to gog) can be one track only.
Better use this or any else normal Windows re-edition disc's\image's to intsall proper Windows version and update
http://redump.org/disc/81014
and patch (for EU version actually)
http://patches.ubi.com/heroes_might_magic_1/

Anyway, better mount cue\ccd\etc disc image file (bin gog or else is NOT an image file, image files is tiny ones and looks like there is no one in GOG build, so i cant say how to proper mount it, CDMage tool required probably to create cue file, again this time better not use anything from GOG, they mess with heroes1\2 releases a little bit more than usual)
to Daemon Tools (Lite 4, not newer) SCSI virtual driver (SPTD driver required), then using Alcohol (120% FreeEdition) to make new image from image.
Only new one mds(+mdf) should be used to install game.

Almost all DosBox releases here have missing dll\etc issues.

As for DosBox'ed executables not have own start link files for GOG releases - just drag-n-drop them exe onto bundled DosBox executable (within same game installation folders or by using your own installed separatly DosBox client - but that reqire few conf-file's editing).

Also, there is something in this article
[url=http://www.pcgamingwiki.com/wiki/Heroes_of_Might_and_Magic:_A_Strategic_Quest]http://www.pcgamingwiki.com/wiki/Heroes_of_Might_and_Magic:_A_Strategic_Quest[/url]
but whole article and this issue description refer to initially wrong GOG build version. GOG version is not a good source.

If there is real compatibility issues (and not wrong actions from GOG or user) - HeroesGL wrapper mod by Verok for Windows version.
Its easier than trying to find best-latest Windows re-editon (dozen of them in many compilations) version and patches.

If you're having trouble with DOSBox, go here, https://www.vogons.org/index.php and ask in the appropriate forum.

Good news!
GOG has finally updated the game and the map editor now works perfectly.
Better late than never, I guess.

The update doesn't work for me. It got rid of the WING.DLL error, but it just launches to a black screen and crashes. There's a pop up, but I can't read it because the screen is black

OK. Just tried installing the game from scratch. The issue you've mentioned happens.
For some bizarre reason if one launches the editor using the Galaxy client it opens without issues. And then the editor always works perfectly, without ever needing Galaxy again.

I suspect that whoever "fixed" the Editor issue, somehow must have unintentionally linked the Editor to some Galaxy activation. I'll try sending a support ticket so that the Editor can be launched only through the offline installers.

To OP:
If you have Galaxy installed on your PC, run the editor through it and it'll fix the issue.