Mosquito problems in Minnesota kind of depend on the weather. If we have a very dry summer, by August they might not be so bad. And if nights get cool enough in September, mosquitoes could be virtually non-existent by then, especially up north. If we have a wet summer though (which so far it's kind of looking like that's going to be the case), mosquitoes will probably be a problem. If you are in the woods near water, mosquitoes are going to be an issue. Just be prepared.
If you are looking for a relatively mosquito-free experience, I would recommend the far southeast part of Minnesota. In particular, around the Whitewater State Park area near Rochester. The website for that park in particular lists the "noticeable lack of mosquitoes" as one of its highlights! It is said that the trout streams in the area are cold enough that mosquitoes have a hard time breeding.