One of my current passions is green roofs and vertical or living walls.
Green roofs are all the rage in Europe. The multiple environmental benefits are set out at Green Roofs Australia's website, which include great insulation for one Rhode island 5 year old hen. Sadly her friend died one freezing night. You may not be aware but you probably have a partial green roof already, with lichen and moss growing on corrugated iron as I found on my very dilapidated garage, or on your terracotta tile roof.
The reality is that in Melbourne, Australia our roofs are not generally equipped for intensive green roofs (as they are in Europe, UK, and some parts of the US), as our roofs are not constructed for snow. But extensive roofs are possible in many cases. The trick is to make sure the waterproofing layer is flawless.
We recently built an extensive green roof on to my chicken shed. It is preferable to overlook a small roof top garden, rather than a swathe of sheet metal. It cost about $90 which consisted of a tin of waterproofer, some treated pine, nails, brackets, plastic drainage layer, weed mat as filter, and scoria, sand and wood chips for the planting medium. I've planted mine up with sedum plants (a variety of colours) as per the photos.