There is no evidence that rats migrate from one location to another depending upon the seasons, as some other animals such as birds to.
In fact, many species of rat rarely move beyond a few hundred feet of their underground burrow or home.
Although they do not migrate, rats will adapt to changing temperatures by going underground in order to protect themselves from extreme cold or heat.
Rats are so hardy, that they are found worldwide in nearly every temperature zone.
The only locations on Earth that are free of rats are Antarctica, with its extremely bitter cold, and some island locations that have been isolated from invading rats.