I couldn’t find anything particularly useful about how to alter MySQL table structure in a situation where replication was being performed so I pretty much had to try something out to see if it worked.
What I found was that MySQL was remarkably clever at replicating changes through from one database to another. I don’t know whether just running a straight ‘ALTER TABLE’ command would work or not but I took the added precaution of running a ‘STOP SLAVE’ command (on the slave) first. Then, once the new column had been added to the master, running ‘START SLAVE’ kicked it off and the database automatically picked up where it had left off by propagating the table alteration and then updating the data.