If you're really careful about removing parts of the wall there, you could possibly save some of the existing wall to use as removable panels that can be put back in place for winter. Or if you don't want to fully remove (and store) them, cut out panels, slap on some trim, and top hinge them to the remaining wall? They can be propped/chained open during summer, and then lowered in winter.Currently, I was thinking to take off the wall with the pop door to make it completely open to the run. My thought is that it would be good for ventilation but hubs is worried that a complete removal will limit options in the future. How I see it? It's wasted space and I want to change that! The only way is going to make it more accessible and open.
Terrible Photoshop incoming:
Cut out blue, save the wood, cover opening with wire mesh.
View from the run. Blue would be the wood panels you saved, either top hinged (or save them to use as inserts), and propped open with a stick or held open with a chain from the run ceiling, to allow for more air flow in summer.