No, cedars do not attract mosquitos; they get this reputation because they naturally grow in wet places, where mosquitos are prone to visit.
However, like any other tree you can expect a few critters like spiders, bugs, squirrels and birds to take home in your cedars. If you’re wary about your trees attracting house guests take the proper steps to prevent that. Don’t forget to use caution when you trim your trees to avoid hurting any animals.