EDIT: Good evening Jim. You beat me while I typed and took a phone call.
My contribution.
As long as you use the
Rename, Move and Copy Files function in MC to move the files, all your Playlists will continue to work fine.
Don't use the Explorer inside MC, or Windows Explorer. If you have extra files beside the audio files, or in subfolders, you may need to move those separately using Windows Explorer. You could try using the "Move all non-imported files in folder with selected media files" in the RM&CF dialogue window, as long as you are retaining the files structure exactly as it is under the new D:\MP3\ folder.
In fact, given the simple change you are doing, where you will be retaining the folder structure and file naming beneath the "D:\MP3 Files\" folder, the best method to use would be to;
Select the files that you want to move and open the RM&CF function.
Untick the "Directories" and "Filename" checkboxes in the RM&CF dialogue window,
Tick the "Move all non-imported files in folder with selected media files" checkbox, if you have any non-media files in the (sub)folders,
Tick the "Find & Replace" checkbox,
Enter D:\MP3 Files\ in the Find box
Enter D:\MP3\ in the Replace box
Click Ok and the files will be moved.
As always, you should run a Library Backup before starting, then test the process with say one Album first, check that all worked correctly, including you Playlists, then run it for a few Albums, and if all is good, run it for the rest of the Library.