The only safe method is a safety harness for a dog, got mine from a pound shop and fixed on on the front seat, gotta say my dog is more friendly than the kids so they get the back seat!
If you worry so much about dog hairs brush it more often, being a working dog does not give an excuse to abuse them but neither treat my dog as a nancy alpha fermale!
A box on the outside of the vehicle looks to me like a 'sweat box' a method of torture and punishment, also open to exhuast fumes etc while on the road!
There again it is not my dog, I don't see great snow levels in NI that requires a husky dog to pull sleigh all year round, a working dog?