Hi Sébastien,
Yes, this is possible within Toad. You'd need to configure the SVN server to use Active Directory and HTTPS. Once you do that, you'd simply need to tell Toad to use WebDAV connection with SSL encryption in the SVN configuration window and then provide your AD username and password in the login prompt within Toad and it should connect just fine.
If you wanted to use Git with Active Directory, you'd need to use a Git server that supports AD. There are a number of Git servers out there, so it would depend on which one you choose. In Toad 12.10, you'd need to handle all clone, push, and pull operations outside of Toad. Once Toad 13 is released, you will be able to perform those operations from inside Toad. You will still need to configure Git's Credential Manager, though, to handle the authentication with the server and keep it updated when you're required to change your passwords.
Since you already have SVN, I would guess that it would probably be easiest to enable HTTPS access and integrate your existing server with AD.
-John