I'm also in MN and have a 6x8 coop with 4 hens. I have a ridgecap/soffet vent system (which is what I assume you are talking about here) and I also have two vents put up in the gable. The ridgecap ventilation works well, but not well enough to be the sole form of ventilation. When we get that REALLY cold snap in January, you know - the one that gives us the -20 business, I close up the gable vents and rely solely on the ridgecap. It tends to get a little stinky in there - mild, but I like to have those gable vents open as much as possible. Since the bitter cold only lasted a week or so this winter, I never did close them up.
The eve vents will be good for cross ventilation in the summer as well as keeping the rain out, but because they are not at the peak of the roof (which is where the hot, humid air will go), I don't really think they'll be enough on their own. But depending on how big they are and how high they are (meaning, if they are by the roost and blowing cold air on your chickens while they sleep), they MAY need to be closed up when the really cold stuff hits. My guesstimation is that you're not going to put your roost at 6 ft high and those eve vents will be out of the way, but I've learned to never assume....
Hope this helps. Have fun.