When I did my diving course, I was told that it was much easier diving in warm waters so if you finish your course in colder seas, you don't have to have a diving skill check before your recreational dive with a new diving operator. On the other hand, if you finished your courses in warm waters, they test your basic skills before they let you underwater.
If I understood correctly, cold waters are considered those that are not in tropical seas so not that chilly to start with but I would like to know where the coldest place that offers PADI diving courses is? That diving school should not be specializing in cold-water diving but should have all the courses, starting with Open Water Diver course.