There is currently no way to snapshot a volume, because by essence, volumes are kept out of the copy-on-write storage. However, this might change in the future, since it's becoming a frequent request.
If you really need that feature in the short term, you could bind-mount a host volume which would itself be snapshot-able. E.g., you could mount a BTRFS filesystem on /btrfs
on the host, then have a /btrfs/data
subvolume, and then do something like docker run -v /btrfs/data:/var/data …
to bind-mount that subvolume in the container.