Our current method for updating public site skins is "comment on the issue with the changes."
This is a bad system for a number of reasons.
We want to put the CSS for the three public site skins we support (Reversi, Snow Blue, and Low Vision Default) in the repository. This will let us open pull requests and track changes.
Note that the changes will still need to be copied to production by an admin to actually become live, but at least we'll have readable diffs for reviewing and a history of the changes in case something breaks.