Those look nicely built, but to me, they are 'more than' a 'run-in' shed! More like a 'self serve stall'!
Seriously--a tip or two---I wouldn't leave the inside 'unlined'; most horses are only too eager to gnaw on any exposed wood, so the exposed 'studs' might not last long at all. Also, anytime there is a 'permanent' opening, it is helpful for it to face AWAY FROM the prevailing winds.
Around here, a 'run-in' shed is usually a three-sided affair, with one side completely open. I have one large one, and three smaller ones....another tip is to make them 'deeper', front to back, than you might think necessary, so that wind-driven weather--rain or snow--is unlikely to 'penetrate' all the way to the back wall, thus giving the horse(s) better protection. The best idea I ever got was to make my large shed 16' deep instead of 12'! Also, mine face the south, so that in winter, the winter sun will shine all the way to the back of the shed during the middle of the day...sure helps keep it drier and cozier! In my experience,facing south, or possibly, east, is generally best. Here, winter winds are mostly out of the northwest, so south-facing the sheds is ideal.
I designed, and my late husband and I built, our run-ins. All are of painted metal panels, with the lower 4' 'lined' with 3/4" plywood(this for minis, of course). Edges of all wood are covered w/ galv. 'corner flashing'; this has worked quite well for us.
Good luck!
Margo