Outdoorsmanhc -- a couple of thoughts for you.
Where is the lake - at least roughly? The winters in the northeastern corner of the state are much more harsh than further south.
It is a little hard to believe that there are carp and nothing else. Contrary to most people's impressions, carp are only moderately resistant to winterkill. For example, yellow perch and especially northern pike can handle a lot lower dissolved oxygen levels during the winter. Of course, the carp may have gotten there by themselves during some high-runoff spring weather, so you could be right.