Minwoo has major issues when it comes to sleeping, and as a result, he usually only gets 3-4 hours each night. And at that, it's usually a very light sleep that can be interrupted by the smallest of things -- such as someone entering his bedroom, or someone making too much noise in the main section of the bunker.
As a result, it's not uncommon for Minwoo to doze off on Youngmin or Hyunseong, although Youngmin is his usual target. While he may love and trust all of the boys, Minwoo really only trusts Youngmin and Hyunseong enough to be that vulnerable and weak in front of them. This is because he knows Hyunseong can and will protect him if something happens, and because Minwoo views Youngmin as the closest thing he has to a real older brother -- one that doesn't just chastise him, but also encourages and loves him and teases him.