We've rented from http://cycletucson.com/ with success a couple of years ago (now we have S&S coupler bikes that travel to Tucson with us each winter).
For locals Feb may be cold, but even though we've seen snow some years, it is [almost] always warmer than home. One year we had a miserable first day -- heavy rain with temps in the high 30s (temp would have still been better than home but with the rain....<shudder />). But we also had some lovely days in the 70s that trip. So we still considered the trip worth it.
Definitely make sure the bike has a flat repair kit. You will need it.
2009 Waterford RS-14 S&S Couplers - Brooks B68-Anatomica - Traveller
2008 Waterford RS-33 - Brooks B68-Anatomica - Go Fast
2012 Waterford Commuter - Brooks B68-Anatomica - 3.5-Season/Commuter
2011 Surly Troll - Brooks B68 Imperial - Snow Beast