How can I load external snippet files into Visual Studio Code?

You could try adding a symbolic link to your shared folder inside %appdata%\Code\User\snippets.

The article Adding Snippets to Visual Studio Code contains more information about sharing your snippets as a snippet extension, using the yo code extension generator. This method might not fit here, because it's basically copying the snippets, but the symbolic link approach might help.

See the article The Complete Guide to Creating Symbolic Links (aka Symlinks) on Windows.