What I tried to do is, select some text and drag and drop it to another MS Word 2003 document. The MS Word document was opened with MS Word 2003. It's really a pain to press control-c and click the MS field and press control-v again and again.
Not directly, as you found out. But if you have a lot of text fragments to copy to a local MS Word, the following workaround might help:
- Click File > Publish to the Web > Publish
- Open the published document in another tab. Drag and drop from that page.
- Click "Stop publishing".
Try pressing Ctrl (on Windows) while dragging.