For DOS, I believe the core was only ever Microsoft or IBM. Some DOS versions bundled add-ons by third parties, but they are hardly essential for operation - e.g. MS-DOS 6 included DEFRAG and MSBACKUP (both licensed from Symantec) and MSAV (licensed from Central Point Software)
Similarly, with Windows, the third-party components are generally inessentials such as certain device drivers, games, some optional system components like the ZIP file support in Windows Explorer-you would still have a usable OS with these bits ripped out. Parts of NTVDM are third-party licensed, although I believe that’s mainly the software CPU emulator used on RISC platforms, I think x86 was mostly Microsoft’s own code
Similarly, with Windows, the third-party components are generally inessentials such as certain device drivers, games, some optional system components like the ZIP file support in Windows Explorer-you would still have a usable OS with these bits ripped out. Parts of NTVDM are third-party licensed, although I believe that’s mainly the software CPU emulator used on RISC platforms, I think x86 was mostly Microsoft’s own code