Metal Roof - I'm not fond of colored, but I have different climate concerns than you do, set upon purlins (basically, thin wooden boards run on top of, and perpendicular to, the rafters). No decking underneath.
The airflow ensures there are limited condensation concerns between thermal gradients (the whole reason felt paper is placed between plywood decking and the actual waterproofing, whether shingle or sheet metal or polycarbonate.
Placing decking increases costs and traps moisture, while preventing visual inspection so leaks. Placing sheet metal essentially directly on plywood (or on purlins, attached to plywood, as when placing sheet metal over an existing shingle roof at end of life) creates no significant dead air space to work as insulation - the purlins are typically only 3/4" thick. That's not much dead air. Metal roofs open from underneath can be leak checked easily and routinely so when they appear, can be corrected early while they are small.
If the underside of your soffits are opened up as free ventilation, and you use a ridge vent, monitor roof, or similar design to allow air to escape at the top, you create a passive ventilation system that draws cool air from lower/shaded locations, warms it as it passes across the underside of the roof, and escapes at the top - which also draws moist, ammonia laden air from the coop.
That said, ridge vents are shallow, and easily plugged by inches of snow - a condition monitor style roof designs address quite well. Not that they are required - you have to look at the total airflow/ventilation package for that - but they do solve a lot of problems (or no one would waste the time and materials building them, except for reasons of aesthetics)
You can also do a half monitor roof, open facing away from prevailing winter winds, if you are looking for a slightly easier, slightly less resource intensive build - but its really not a big difference.
