I'd steer away from those turbine vents for this kind of situation. (Though they are great for some other situations, like haylofts and attics, where you have a much larger space but no ability to have 'holes in the walls')
First, the only time they offer any greater benefit than a simple roof vent is when the wind is blowing, but you know, if you can have any meaningful amount of windows/vents on the walls, THOSE provide better ventilation on a breezy day ANYhow.
Second, yes, rain and snow will come in, and cold air will dump down right onto the roosting chickens (b/c your coop is small), unless you plug it up in wintertime, in which case what was the point again?
If you have SO many windows (do you have pics by any chance?) then summertime ventilation should not be a problem; the only problem is ensuring winter-worthy ventilation too, and (pics please?) you really SHOULD be able to achieve that by making vents at the top of the walls either over top of the windows, between the windows, or in the soffits (roof overhang).
So personally I would suggest that if you HAVE to cut a hole in the roof, just do a regular attic vent not one of the whirly thing (just more to blow off in a storm and you won't really get much of any *benefit* from it in your situation, with so many windows); but you may well not need that, just find somewhere to stick in normal passive ventilation openings of a sort you can use in wintertime, and rely on windows for your extra summer ventilation needs.
JMHO, good luck, have fun,
Pat