I like this! Very cute! You could even put some hanging baskets along the front rafters.
I have a couple of questions. What is on the roof, under the poly panels? Is it hardware cloth? Reason I ask is because it looks like there is a gap where the rafters lift the panels up off the roof. If it is hardware, that would make great ventilation. I would think about adding something along the raised portion to keep stuff from getting trapped between the cloth and poly panels. Leaves, debris or birds even.
I agree with jajeanpierre. I wouldn't use the clear poly panels. Looks like it would give it a "greenhouse" effect, make it much too hot for our Texas weather. Maybe white or tan since you don't want to get the darker ones. Or, you could get a color to match your trim.
You could put another window along the back wall. Make it much cooler during the summer and just keep it closed on those cold winter days.
The base is 5x10, so that would give you a max of 5 hens maybe? You could probably make the run a little longer without costing much more if you wanted to or even add to the run later. Looks like it wouldn't be too much trouble.