While he knows she will probably hate him for it, I do think the Snow King decided to burn the scroll to protect her. She's told him repeatedly that she continues to work with the Emperor and gamble it all so she can find a clue about the spirit people. I think he's worried that she'll get herself killed in the process. Moreover, there are hints that she committed some kind of mistake in the past that I think led to trouble for her people so I think there is some concern about her learning the truth and regaining her memories. All together, I think he believes she'll only hurt herself more in the pursuit of the spirit people, so if he eliminates that information, he hopes she'll give up this quest and live peacefully.