Historically speaking, this is actually a very old topic [ame=http://en.wikipedia.org/wiki/Acclimatisation_society]Acclimatisation society - Wikipedia, the free encyclopedia[/ame]
"Acclimatisation and Breeding" by Carl Hagenbeck
etc. etc.
In general, the ability to adapt to weather different to that of the original habitat is defined by the metabolism of the animals, its anatomy, behaviour and the climate of the original habitat. A bigger mammal from a native climate with hot days and cold nights (f.e. Addax) or one that might even venture into colder areas (f.e. Common Eland) is more likely to adapt to cold weather than, say, a naked mole rat. Large, cold-sensitive acra (like the ears of Bongos, Okapis or Elephants) can easily sustain frost damage and thus limit the outdoor husbandry of such species, while freezing surfaces can lead to downfalls and traumatic laesions. Frozen water mounds can lead to animals escaping, cutting themselves on the ice, and even drowning.
Cheetah drowns after falling through ice - Panorama News - Austrian Times Online News - English Newspaper
I do support your point of view, @Arizona Docent, but I have to agree with @Hvedekorn
that the average zoo visitor expects to see exotic animals in a typical zoo. Wildparks with mostly native (and some cold tolerant exotic) species are pretty popular in Europe, but hardly ever (with some exceptions) reach the visitor numbers observed in typical zoos. Additionally, quite a bunch of native European species are actually a lot harder to keep and maintain in captivity than the "average exotic", such as lion, blackbuck or flamingo. Similar things can be said about some native American species, such as pronghorns.
In return, animals from a cold native climate are less likely to adapt well to hot tropical weather. Think of muskoxen, gyrfalcons, snow hares etc. etc. not really "blossoming" in (sub)tropical zoos...