Designated trout lakes are just that, designated for trout only. They may have other fish but you cannot legally fish them for any species outside the designated trout lake seasons.
A non-designated trout lake is the same as fishing a lake in April for crappies when it has walleyes, pike and bass.
As the previous poster said, you cannot legally target a fish out of season. Doesn’t matter what it is. Incidental catches are obviously ok and you must return them to the water. The DNR does state that you can legally take pictures so long as return it immediately to the water. It can’t be put in your livewell, you can’t leave it flopping on shore or the ice for 5 minutes. The DNR will think you have put it in your “possession”.