As touched on before, Edvard Munch was a relentless experimenter with materials, techniques and styles. Interestingly, he also experimented with letting his paintings "mature" by leaving them outside, exposed to wind, rain and sun. The essay 'The Weathered Paintings of Edvard Munch' (PDF) recounts how Munch called this the "kill or cure" treatment or the horse cure ('hestekur' in Norwegian).
Of course to some extent all art undergoes deterioration - especially outdoor art like sculpture and murals - but usually this is seen as an unavoidable evil, to be fought against by conserving, restoring and protecting the artwork. Munch was one of the first to use the decay caused by the elements as an aesthetic strategy, both to give his works a weathered, gritty look and to introduce the idea of time and chance into the creative process. (Ironically this now poses strange dilemmas for conservationists of his work.)
More recently, another artist who explicitly used weathering is photographer Hiroshi Sugimoto. As part of his 'Seascapes' project, he permanently exhibited a number of photographs outside, at the Benesse House Museum on Naoshima, Japan. This created the interesting contrast between virtually timeless images of water, light and air, and prints deteriorating from the influence of those same natural elements.
While Sugimoto's motivations may be more philosophical than aesthetic, what he has in common with Munch is that they both use natural decay - or maturation, however you want to look at it - as a way to visualize time. In the 20th century chance and randomness have been employed in art in all sorts of ways, but the simple idea of using the weather is surprisingly rare.