Woods design really boils down to two issues. Creating an air container sealed on three sides during winter, which creates the still cushion of air at the north end of the coop, where your birds should roost, and harnessing the power of the sun for warmth in winter, through the use of the passive solar technique of leaving the south end of the coop open, to the low winter sun in the southern sky.
In the summer, opening the windows on the east and west sides of coop, breaks the seal of the container and creates cross ventilation, which is cooling, and in Woods design, even goes one step further by allowing the opening of the roof top windows, which creates an upward circulation of air in the coop.
As the cooler air enters from the lower level windows, it's exhausted through the upper windows as the air warms and rises.
These two factors are the genius of his system, he's harnessing the power of natural forces with his design.
Chickens have three requirements from their environment if they are to thrive. They must be kept dry, they must have lots of ventilation, and they must be kept out of the wind.
You'll notice being kept warm is not on this list. A chickens normal body temperature is 107 degrees, they are designed to live in cold weather. They can handle the cold weather, just like all the other birds we see around us living in the wild, even in the coldest temperatures we experience at our homes.
The natural forces Woods utilizes are predictable and before the advent of central air and heat systems, these principles also drove human architecture.
As Howard points out, Woods was well aware of all these methods in his design. He's done the work for us.
It's a law of physics that creating a sealed structure on three sides prevents air from moving, once you're a few feet into the structure the air is locked in place preventing drafts, but still providing great ventilation because one side is completely open with just wire. That's one of the basic requirements of the birds, great ventilation.
Leaving the open side facing south is a function of two important facts.
First the sun in winter hangs very low in the southern sky, in fact the sun is so low, the sunlight doesn't even come from overhead, it comes in sideways from the south side. The power of the radiant energy from sunlight is much more than most of us realize, and gives your birds a huge benefit in warming.
Second, the vast majority of cold wind comes from the north, northwest, or northeast. Placing the open end of the coop south, turns the coops back on those cold winter winds, and leaves it open to any warm southern winds.
You'll also notice Woods preferred long rectangles for his buildings, with one of the short sides facing south. A rectangular shape creates a larger cushion of still air on the north end of the coop, as opposed to a square, because rectangles present less wall length to the wind.
Woods did a lot of experimenting, and determined even in the worst blowing rain from the south, the rain never penetrated more than three feet into the building, with the wind itself, not penetrating much further than that either.
That's why we're seeing Woods proposing dimensions like 6'x10', 8'x12', 8'x16', 10'x20'.
He mentioned he wouldn't recommend a single chicken house larger than 20'x20', and even then, he mentioned it would be wise to divide that coop down the center, creating two 10'x20' bays, that only connect to each other a few feet back from the open southern window, allowing the chickens the use of both bays.
He always recommended placing the roosting bars at the north end of the coop, deep in the cushion of still air at the back of the coop, which is an area guaranteed to be draft free.
After all this background you can understand how and why he harnessed all these natural forces to meet his goals of a dry, draft free, well ventilated house for the chickens.
If you follow his recommendations, you're going to create an excellent environment for your chickens to thrive.
Coming back to the crux of your question though, is this design compatible with your goal of simultaneously using this structure for birds and as a greenhouse?
Unfortunately the answer is no. The problem is the chickens and the plants have opposite ventilation requirements, which can't be met unless they are physically separate from each other.
Greenhouses create a warm environment for growing plants in winter by cutting off ventilation, and using solar gain to heat up the trapped air.
This is opposite to the good ventilation chickens require.
On the other hand, providing the good ventilation chickens require, will allow the trapped warm air to escape, making it too cold for the plants, with the cold not being a problem for the chickens as we know.
The Woods is a top notch coop, the best in my opinion, but I think you're going to need a separate greenhouse.
The idea of ever cutting off the ventilation of a Woods House by blocking its southern open face, is the equivalent of removing your cars engine, and expecting to be able to drive it to work the next day, it doesn't work anymore, the engine is gone, the car is broken.
Good luck with your project, you're doing the smart thing, researching before building. You're going to be building a great house for your birds and avoiding all the mistakes we've made at the same time.
I've had great luck with my flock of 13 birds, only because of the help and knowledge others have shared with me here over the last year. I started with zero knowledge about chickens and have avoided a ton of mistakes because the help offered here.