Haha I'm oop north too, originally a southerner! It's not so much the cold I have a problem with, but the wind. How it howls up here!
I bought 'one of those cheap chinese imports', because there was no way we'd be able to build something even a quarter as good for the same price (£145). So what we've done is insulate it (rolls of the thin silver bubblewrap stuff from B&Q - two layers where I remembered), then ply and caulk the inside for the same reason you are. I hear about so many brits buying these coops and sticking chickens straight in. Within no time they have red mite and rotting wood, then they complain about the quality... *sigh* I wish more would come on here and read all the common sense. Caulk and paint! So simple!
BTW, there are loads of special offers on the fiberglass insulation atm. Pop to Wickes; they have a buy 1 get 3 free on!
Ultimately, yes I would insulte. Just because you can't change your mind once you've put the siding on.