Goat house between trees - ideas?

I have some nice small oak trees in a roughly rectangluar shape so I was thinking, why not enclose them to build a house for the goats. 

I was planning to just leave the floor as dirt as it is not a wet area and then putting some hay in there. 

For summer (ie now) I could build up walls with small logs and then cob between them for winter insulation. 

I'm really not sure about the roof as I think the goats will jump on it so it should be strong.  Any ideas? 

Please let me know if this whole idea is crazy and I should just take out the trees and build a structure.  I like the idea of keeping the trees but I'm not sure how to do it.

It can be done and it can work but you need to remember that the trees will continue to grow and change shape. We had a big birch growing through part of our cabin when I was growing up. It required cutting out a little of the floor and roof every couple of years to keep the tree alive and so it did not grow around the wood. If you design it to allow for this you could leave them there.

The other option is to keep them. Build the shelter using the trees as your corner supports. Then girdle the trees. This will kill them but keep them standing in place. You now have you foundation and supports.
The trees are dead though and branches will eventually start breaking off.