I think the answer is yes but I will ask anyway. Does the card u draw for kings of summer count against your draw cap.

Another stupid question but if it's winter and I draw one less does my draw cap go up by one.

The card you draw through Kings of Summer DOES count against your draw cap.

The card you do not draw due to Kings of Summer (while it is winter) does NOT increase your draw cap because it is preventing you from drawing that card through the Draw Phase "Draw 2 cards" framework. Those two cards do not interact with the draw cap.