The Owl is a pet in Harvest Moon: The Tale of Two Towns.
Owls are not accessible until Year 2. After that, you can buy one from either of the animal shops for 10,000G. There is only one choice of color for your owl. The owl will take you back to either town from the top of the mountain. Although Kana/Grady will say it requires training, it doesn't. You can buy Owl food at the general stores.
To use your Owl stand on the wooden platform at the very top of the mountain (on a clear day) and press A to call the owl to take you down the mountain. Your owl will not pick you up during snowy, rainy or stormy weather.
Once you are good friends with your Owl, it will sometimes sit on your head. Your owl doesn't have a home that you need to build for it, it will just fly around your farm when not being used. Owl treats will sometimes show up at the general store.
Like all other pets, the owl will never get sick or die. Buying food is optional, but you forfeit your relationship with the owl.