You must use remote folders. If you create a remote folder pointing to the WebDAV resource, you will able to copy, cut, paste, drag and drop,… without problems, instead of the operative system (Windows, Linux, MacOS).
Opening or saving from applications or suites it is different: these applications or suites have to support WebDAV commands: MS Office and Open Office support WebDAV resource as you were working in a local resource; Notepad or Acrobat Reader don't support WebDAV. Linux (and I think MacOS) tools have often better WebDAV support.
I'm using WebDAV with gigas of document data and I have no problem (Alfresco 2.1 CE).