This document explains why you will not be able to browse a root share on Windows 2008-R2 and Windows 7 onwards operating systems
With ASA WebVPN you will not be able to open Windows 2008 R2 server share list using CIFS protocol.
The same will happen with shares on Windows 7.
This is because the ASA CIFS implementation uses MS-RAP (MS Remote Administration Protocol) to enumerate the shares on the servers. MS-RAP protocol has been discontinued starting from Windows 7 and Windows 2008 R2 operating systems.
To verify, configure captures on the ASA interface connected to the server. In the captures you will notice
Trans Response Error: STATUS_NOT_SUPPORTED immidiately after EnumerateRequest for \\server\IPC$.
Browse to a specific share and not the root share, so \\server\share will work but \\server\ will not work.