I don't know what WebDAV has to do with your question.
I hope you realize that the deal with "extensions" is that they are computer programs that run on the web server. Instead of calling them "extensions" Expression Web uses ASP.NET technology. DreamHost doesn't support ASP.NET or Mono.
WebDAV is not related to the "extensions" issue. It is a method for sharing files online.
If your web site is interactive, such as processing form pages to access a database or send email messages or other actions that depend on a web server program, you will also need to develop for an alternative to ASP.NET, such as PHP, Perl, Ruby, Python etc.