Hello Becky!
I would think a 'snowbird' is anyone who stays South for more than just a vacation (ie., a 2 or 3 weeks). Whether renting or owning ... I don't think that would matter. Just me own opinion. I am a very recent snowbird (1st time starting this year... last week of December through April 2008), so I'm no expert, by any means.
Rebekah