"A goat tower is a multi-story decorative goat house, modeled on a European garden folly, an early example of which was built in Portugal in the 19th century. The first goat tower was built at Aveleda, a winery in Portugal's Vinho Verde region. Since 1981, several other goat towers have been built in South Africa, Norway, the United States, the United Kingdom, and Argentina; these include three at other wineries. The towers typically are multi-story with climbing ramps spiralling the exterior and often become tourist attractions"
How feasibility would this be in the middle ages, in particular the spiralling ramps? The actual tower itself seems reasonable to construct. However getting someone to fund something like this back then would be difficult I imagine. I know goat welfare wasn't a priority back then.