Templates are like most (content) items exposed through WebDAV. For Compound Templates (aka. Modular Templates), this means the XML source of the template is exposed in WebDAV with their own specific extension.
Page Templates will have
.tptcmp and Component Templates
.tctcmp for example. You can very easily store these outside of Tridion as they are basically text files. However the WebDAV URLs used in them need to be available on the system where you import or create them, if trying to do so via WebDAV.
I myself find it most of the time easier to create and maintain Page and Component Templates through the Template Builder than trying to see them as XML or text files and use an external editor for them. Personally if I needed to safeguard them or copy them across from one environment to another, I would just use Content Porter. But you can do the same via WebDAV.
When talking about editing Template Building Blocks, specifically the Dreamweaver design TBBs (exposed as
.dwt) then these can be edited by any WebDAV capable editor. As the name refers to the original idea was that these templates should be edited with Adobe Dreamweaver, but you can just as well use any other WebDAV capable editor. I'm unsure if Visual Studio supports WebDAV directly, but when you map a drive to the WebDAV location, you can use that no problem.
The nice thing about Adobe Dreamweaver is that is stores a local copy of the WebDAV file and has a way of automatically syncing your local copy changes back to the WebDAv server (SDL Tridion in this case). So you could use the local copy to check it in an SVN and use Dreamweaver to sync. Else you have to manually sync them from your SVN to Tridion using any WebDAV client.