Get back in touch with me when Docker can help with Windows deployments. (Is there an issue I can 'star' or otherwise track?)
Edit: To say Docker is analogous to Git for deployment fails outside of the Linux server realm (lxc). I'm trying to think of an OS-specific source control system to fix the analogy but can't come up with anything only-Linux... 'TFS for deployment'? :)
Not sure I would call it thin, but today Docker uses LXC as a container provider. But in saying so it misses the point of Docker. Keep in mind also, this is all related to the daemon. Full client capabilities are available on any platform today.
In a previous blogpost, the Docker team outlined how LXC will become a (albeit native) plugin, just like AUFS. Running Docker on BSD (using Jails as the container provider) is certainly a goal. If you're on OS X, you could use chroot instead of full namespacing capabilities.
To be fair, this is not available today. But I don't think it's fair to say that Docker will not be useful anytime soon on those environments.
The underlying technology for Docker is LXC (Linux Containers), which is very tied to an underlying linux system. I would expect Joyent to support enough for Docker to work in SmartOS before MS would/could in Windows.