After finding the map editor application within the game folder I tried to run it. Initially it was popping up the error:

"The code execution cannot proceed because WING32.dll was not found. Reinstalling the program may fix this problem."

Of course the first thing I tried was uninstalling and installing it a couple times but the error stayed. Next I searched my computer for WING32.dll. I found the Program under C:Window/System32 and if i moved the file from there into the game folder the error message changed to identify that the program A.) was in the wrong folder by being in the game folder and B.) that the correct folder for it to be in was C:Windows/System32.

I have reached the end of my knowledge to try and find a solution, any suggestions?

EDIT: I am running Windows 10 (32-Bit) and I am running the DOS verison from GOG.

Checkout this thread
https://www.gog.com/forum/heroes_of_might_and_magic_series/graphic_gl_wrapper_for_all_heroes_heroes_of_might_and_magic_1_2_3_4_and_chronicles_for_better_wo/page1

Original thread here https://verokster.blogspot.com/2018/10/heroes-of-might-and-magic-i-iv-gl.html

This about GL Wrapper which replace WING32.dll. Just download patch, axtract it via 7zip, and copy WING32.dll into game folder near EDITOR.EXE

This can be as easy as downloading gl wrapper from post above or might not be as easy.
I remember having similar issue with homm2 on win xp (32-bit). Game runs fine on xp without wrapper, but still, I had to copy/paste wing32 from game iso into system32 folder for it to work. For homm1 it might be that your game directory is not on the same drive where your windows is. One time on win10 (homm2) I had an issue, that my game froze if I changed some game settings. Turn's out that the directory where I installed the game had some windows rights restrictions and game exe could not change whatever files to save new settings or even change high-score files. With these old games it can be whatever crazy issue you can and cannot think off.
You should specify what kind of OS you're using and if it is gog's version or iso backup... You should try one and the other to compare. Is it only the editor that is not working? Try out gl wrapper. Try to change install directory. Try to obtain wing32 from source installation and copy into system32 and sytem folders. Try different computer :D

So this helped with the initial problem but now it is saying it cannot connect to my CD drive. This is really a problem since I don't even have one.

Here is NO-CD for Win version of HoMM v1.2. Use it together with GL Wrapper (press F4 - for windowed mode)