A .dwt file affects html files only through dreamweaver. Every change will have to be applied to all the pages affected by the template through Dreamweaver, then the files must be uploaded again. For your header and footer situation, I would recommend sticking to .php.
When editing a page through dreamweaver, it nicely restricts users to
only edit within the set confines of editable regions. For example, I created a template for various university departments to utilize - they could edit the content but not the formatting.
One template should apply to many pages (or subtemplates), so naming them like that would not be ideal.
And basically... if you are the only one maintaining the site and know how to use PHP includes, I would ignore DWTs. They're useful for the right situations, but maybe not yours.
