There is no legal definition, so certainly this is a question on which reasonable minds can differ.
There is an
argument that
any aircraft type that has seen military service is a 'warbird', whether or not such service was 'active' or not. Thus, Tiger Moths, Chippies, Harvards, Stearmans, etc. are all 'warbirds'.
Is there any real harm to being as inclusive as possible? I can't think of any. Martin Caidin discussed the 'warbird' definition issue at some length in his book
Ragwings and Heavy Iron: the Agony and the Ecstasy of Flying History's Greatest Warbirds, and (as I recall) he argued that a narrow definition would (i) promote undesirable snobbery and (ii) exclude many people who might otherwise start off with relatively cheap L4 type airplanes and eventually 'graduate' to bigger, faster, sexier (and far more expensive) 'warbirds'.
P.S. Some people even claim that the Ercoupe is a 'warbird' (!!!); see
here