Not American but doesn't central America get cold as fuck at night? I would assume that's what cowboys dressed for since you can always remove clothes but you can't exactly create them from thin air at night.
I'm not an expert, but I believe it's more of a North American thing (Canada, U.S.A., Mexico) due to the mountain systems along the three countries. The Rocky Mountains, the Trans-Mexican Volcanic Velt, etc. are all part of the North American Cordillera. This, and the occasional deserts.
I'd guess ponchos, jorongos, and similar pieces of clothing were adopted by non-native settlers (Spanish, English, etc.), including non-native cowboys, because they are good against the changing weather during the day and the cold nights, as you said.
I mean, Central America must have cold spots along their own mountains and South America has the Andean Mountain Range (enormous system), but I do not know about their traditional clothing, except they share the poncho, and I do not know which of their clothing we still wear to this day.