My first thoughts on positioning a coop and run center on drainage. Don’t put them where water drains to them or especially where water stands. To me that is more important than anything else.
I assume your main winds come out of the west. That would fit most people in Ohio but I live in a north-south valley. My winter winds normally come out of the south, strange as that sounds, but some do blow from the north. Very seldom do I get anything from the east or west. It’s always possible localized terrain features can make yours different than my assumption of from the west. You may have trees or other buildings blocking winds.
How high are those vents? Are they over the chickens’ heads when they are on the roosts? In Ohio you are going to get some fairly cold weather. In cold weather, you don’t want the wind hitting them when they are on the roosts no matter what direction the wind is coming from. As long as they are not hit by a direct breeze they can handle your cold weather fine with their down coats. If the vents are over their heads any breeze that develops will be over their heads.
In summer the more ventilation the better. It doesn’t matter if a breeze hits them.
I still haven’t answered your question have I? I don’t think it matters that much as long as a breeze is not hitting them directly in the winter. Most of your winds probably blow in from the west but your coldest winds are likely to come out of the north. They can come from any direction. Same with rain. Most of your rain probably blows in from the west but it could come from anywhere.
I don’t know what your vents look like. Do they have shutters or something to keep the rain out or is it just a hole cut in the wall with hardware cloth over it? What does your coop look like? Will it dry out rapidly if rain or snow blows in? If that is all the ventilation you have and your coop is very large it may not dry out that rapidly.
If you do have a predominant direction rain usually blows from position the coop to minimize that, which probably means north-south. But I’d be more concerned on how the vents are positioned on your coop from the effects of a winter wind hitting them than on coop orientation.