I looked at different roofing materials when I was building our brooder house. Metal is expensive, but it holds up way better than any of the fiber type roofing materials, and it will sheet off snow and ice much better. I think it is worth the price to use metal. At Lowe's I paid about $16 per sheet of 2'X8'. What are the posts you have for your pens? They look round. Are they sunk into the ground? If so, how far. If they are sturdy enough, maybe you can use those as the support to attach to and it would cut down on some of the expense. You don't have to use OSB underlayment for the roof if you have strong enough cross pieces (I think they are called purlins) to attach it to and be able to secure it all the way to the edges so you don't get the wind catching it and flapping it or tearing it off. I know it is pretty open at your place from the pictures on your sight, but I don't know how strong of winds you get there. Here in Minnesota you have to tie everything down that you don't want blown away.
theri