Actually, Cirno can be fairly clever (no pun intended)! Go read the dialogue for the great Fairy War. She references old quotations and makes smart-alecky remarks. She's just way too overconfident and has a childlike view of the whole world (probably not too good at things like mathematics and such). Her stupidity is exagerrated a lot in fanon. Even ZUN, who called her a baka in the first place, gives her clever dialogue!
Don't the picture and the signing highlight the fact that there is a questionable looking stain on her sheets? without leaving any doubts as to who caused it?