I have to come out as strongly against!
It can be cold in an open cockpit. Also, when you are done taxing in the rain, you can get wet. The wind is horrible (Depending upon the airplane. The YPF-7 Waco I had time in was calm - you could lay a sectional on your lap and it would stay. Stearmans without a modified turtle-deck you can't do that in). Also..THE NOISE is horrible...and I am not talking about a sweet running horizontallly opposed engine either, but noise from those nasty, cantankerous and loud radials! Also, don't under-estimate the likelyhood of falling out! I would be interested in seeing the numbers on how many people have spontaneously fallen out of open cockpit airplanes for lack of a roof. Also, for a brief time years ago, flying in an open cockpit airplane turned me into a cross-dresser (it was so cold delivering a Great Lakes with a friend during the winter that we actually went to Wal-mart on a fuel stop to buy pantyhose which supplemented our clothing for warmth - meaning that for the last half of the trip we were flying drag-queens.
All in all, because of the cold, the wind, the noise, chances of falling out, and possible conversion into a cross-dresser I would say to you not to chance it.