I have birds that I keep outside in the summer, sometimes they will just sit in the rain even though they have plenty of covered areas. All birds have an oil gland that they use to run an oil over their feathers to keep them in good order and different levels of waterproof depending on species. Most birds can sit in the rain for a while without actually getting wet.

But ya, birds can get wet and cold but they are usually adapted to their environment to not get too cold or too wet.