This is possible now, though in a bit of a roundabout way.
You can create such a field on the Contact form and it will be copied into each event registration - and can subsequently be edited there.
What we do not have is the ability to search on these fields via Advanced search (Currently Advanced search only applies to members) but we are working on this and it should be released in version 3.1
Dmitry Buterin, Chief Apricot