Heat butter in a large skillet over medium heat. Add oxtail and onion; cook until oxtail is browned, 5 to 7 minutes per side. Transfer oxtail and onion to a slow cooker.
Pour wine into the skillet and bring to a boil while scraping the browned bits of food off the bottom of the skillet with a wooden spoon. Pour wine mixture into the slow cooker; add water to cover.
Cover and cook on Low for 8 hours. Add potatoes, carrots, celery, and green beans; cook soup for 4 hours more.
Cool soup slightly; refrigerate until fat has risen to the top and solidified, about 1 hour. Scoop off fat; stir in tomatoes. Reheat soup before serving.