Growing up on Tennessee I saw chickens sleeping in trees when it never warmed up above zero Fahrenheit for several days straight. That was brutal, we were not used to that kind of cold. Those chickens were not sleeping on a bare tree branch overlooking a bluff squawking defiantly into the teeth of a blizzard, they were in a sheltered valley in a thicket, pretty well protected from wind. They did not sleep in a huddle keeping each other warm, they relied on their insulated feathers to do that. I will point out that they had great ventilation.
You do not need to give your chickens a warm place. You need to give your chickens a place where they can keep themselves warm. You do that by keeping them dry (good ventilation is important in this) and giving then a place that does not turn into a wind tunnel where they are. There are different ways to do this but the way I like is to have ventilation above where they sleep. That way any wind goes right over them.
I don't know what that shed looks like, doors or windows. It is unlikely to have any real ventilation up high and unlikely to have any roof overhang so you can just cut holes and cover with hardware cloth to keep out predators. You might consider gable vents with louvers or, if the roof is strong enough, a roof vent.
In addition to ventilation and a run, you will need to install a nest, roosts, and you probably want a pop door. That is a small chicken-sized door they can go in and out while leaving the human door closed. That helps keep rain and wind out of the coop. That shed is probably going to be pretty expensive and will not come with a run. In your position I'd consider looking at the coops in the Articles tab above and select one you like. Many of them have plans and instructions. Then get a quote from a handyman to build one for you. You may find out that the finished product will suit you better and maybe not all that expensive in comparison.
Good luck!
