Katsuki was feeling a little sick lately, but he hid it well from everyone because he didn't want to seem like a baby for being sick, that was one thing you hated about him.
You two were just chilling in your room, on your bed, you both were just sitting in comfortable silence, doing your own things, when you decided to hold his hand, and he let you, because this wasn't unusual. His hand was cold. That was an immediate sign for you that he was sick, because he was usually hot because of his quirk, his hands and rest of his body was usually hot. And because he was sick, his body was slightly shut down, so instead of the usual burning up, he was cold. You just continued on with what you were busy with, and he did too, until you decided to speak.