He pitched in Chicago, which can be cold in spring and fall. I'm not sure the weather thing is as big a deal as you're making it. No hitter likes to hit in the cold either. I dont remember too many instances where a GM backed away from a player because of how the player would handle the weather in the new city.
I agree with you he has health issues, although the one good thing for Sox fans is that last year he put up 219 innings and had a hell of a year. 3.37 era, 1.09 whip and he finished 10th in the AL in FIP, just ahead of Weaver and Kuroda.
As for this year, yes his era is 4.28. But if you take out his worst start of the year - the one in which he pitched with a fractured rib- his ERA isn't quite as bad. Going into that start, he had a 3.62 era and a 1.09 whip through the first 10 starts of the year.
So in closing with Peavy, he is still a very good pitcher, a very solid 3 and if healthy down the stretch maybe even a 2. Health will be the question. The good news is his injury this year wasn't arm related.
Also keep in mind that they also have him under control for all of 2014 AND the fact that they can give him a qualifying offer and get a draft pick out of it should he leave after 2014, that makes it even better. Neither of those things apply to the rangers who traded for Garza, who will be a FA in a few months. And they can't offer him a QO and will get no draft pick when he leaves.