I kind of got the impression that the Faerie Kings tended to be Wildfae, rather than associated with their courts of origin. At the same time, they tend to reverse the stereotypical aspects of their respective courts.

The Erlking is the Summer King, or at least one of them, but he seems like he would be more in tune with Winter. However, The predatory nature of he Winter Fae stems from scarcity. It is the wolf in the snow, perpetually one day away from starvation. The Erlking is not a starving wolf, he is a well-fed lord, hunting for sport and the thrill of the chase.