The "WebClient" Service seem to be not running  on the client.
A good information/whitepaper about "Sharepoint Explorer view" can be found under www.microsoft.com/.../details.aspx, with explains that WebDav protocol has 2 "types" and different applications use these 2 types different.
For Adobe Acrobat Reader i found a interesting solution here www.omtool.com/products/swiftwriterPlugin.cfm.
But this tool works only with webdav and as the whitepaper tell us, this is only working over http and not over https connections (Windows XP).