Go to your back door and look for the dog.
If the dog is at the door and he is wet, it's probably raining.
But if the dog is standing there really soaking wet, it is probably raining really hard.
If the dog's fur looks like it's been rubbed the wrong way, it's probably windy.
If the dog has snow on his back, it's probably snowing.
Of course, to be able to tell the weather like this, you have to leave the dog outside all the time, especially if you expect bad weather.