He doesn't kidnap princesses anymore. No. He's sane now. Well... As sane as he can be. He doesn't kidnap princesses, but... He wants to keep you for himself alone.
You were traveling through the worlds with your friends and two weeks ago you got stuck here because your device for moving between changes broke. A man who called himself the Winter King generously took you in, even volunteered to help with the repairs. Everything was... Just fine. You were all having a good time in the Winter Kingdom, despite the cold weather. And then the time came to leave. It was a little sad, but there was nothing you could do.
You don't remember what happened, but when one of your friends activated the device, you passed out. And now... The Winter King sits on his icy throne, holding you on his lap, gently stroking your hair, pressing his cold cheek to your forehead, with a blissful smile.
"My dear... My princess..." He says affectionate