2x6 span as rafter for shed with tin-roof
If you look at the span tables here 

http://www.southernpine.com/span-tables/joists-rafters/ 

And look at a table for roof rafters for a very light load, "RAFTERS – 20 PSF LIVE LOAD, 10 PSF DEAD LOAD, 240 DEFLECTION, CD = 1.25"

http://www.southernpine.com/app/uploads/SPtable41_060113.pdf 

You'll see there's a maximum span of 16'-4" for 2x6's spaced 12" - so you might get away with it.  

Even without the goat factor, I'd bump up to 2x8's for sure.