WebDAV does not open folders for wich url alias based not on object name.
If we define for Folder class custom URL alias name pattern <nice_url|short_name|name> and fill text attribute nice_url with some data,
WebDAV would not find such folder. The method used to access node in WebDAV is based on using language translations of node name,
but for such configuration no such alias will be created.
The possible solution is to fix WebDAV directory listing routine to show url aliases, but not translated node names. Not very good solution, but it works.

Steps to reproduce

install with plain_site.ezpkg
1) modify Folder class, filling URL alias name pattern with <nice_url|short_name|name>
2) add text-line attribute nice_url to folder clas
3) add folder object with name "Folder-1" and nice_url "good-looking-folder". URL alias will be /good-looking-folder, and folder will be accessinble using this address via http
4) try to access the same folder via WebDAV. Folder will be showed as "Folder-1", but attemt to enter it will fail because no such url alias for this folder exists.