Why does Liesel blame herself for Max's illness in The Book Thief?

It's Christmas Eve and the children are full of the good cheer of the holiday season. Liesel brings pots and pans full of snow downstairs to the basement where Max, a young Jewish boy, is being hidden by the Hubermanns from the Nazis. Liesel wants to bring some of the outside world into Max's life. Max spends all day cooped up indoors to avoid being captured by the Nazis, so Liesel thinks she's doing him a good deed by bringing in some snow. Max seems to agree, as he and Liesel indulge in a snowball fight; even Hans and Rosa Hubermann join in the fun. They also build a snowman together—though, of course, it soon melts.
However, joy soon gives way to sorrow; from that day, on Max's health deteriorates quite rapidly. Liesel blames herself for Max's illness; she thinks he must've caught a nasty chill from all the snow she brought inside on Christmas Eve.