At the very beginning of chapter eight, it states that according to Mr. Avery, unusual weather was caused
"when children disobeyed their parents, smoked cigarettes and made war on each other."
Now, Jem and Scout, being young, were a bit freaked out by this statement; they had, after all, disobeyed quite a bit and actually outright lied when it came to some of their Boo Radley adventures. So, when cold weather came to Maycomb that year, for the first time in a long time, Scout says that "Jem and I were burdened with the guilt of contributing" to that rather unusual cold snap, because they had believed Mr. Avery's rather punitive statement about the weather. I hope that helps a bit; good luck!
Jem and Scout are suckers for superstitions. They believe anything a neighbor says about something that they don't know much about. In fact, the whole town shows that it is superstitious by the way they treat Boo Radley, as if he were some boogieman rather than a poor shut-in. For example, children won't eat the nuts that fall into the schoolyard from the Radley's tree, black people won't walk by the Radley house at night, and Calpurnia spits when Mr. Radley walks by. When it just happens to snow for the first time in Scout's life, she thinks the world is ending. The interesting thing about it is she doesn't hear from anyone that God is punishing Maycomb when it snows, which is what one might expect from living in the Christian Bible-belt. No, the kids only hear that Mr. Avery "said it was written on the Rosetta Stone" that the seasons would change "when children disobeyed their parents, smoked cigarettes and made war on each other" (63). Jem and Scout had not done the last two on the list, but they sure had disobeyed Atticus by playing out the Radley family history in the front yard and trying to get Boo to come out by taunting him.
Because Scout and Jem are superstitious in their young years, they also feel guilty for "contributing. . .[and] causing unhappiness to our neighbors and discomfort to ourselves" (63). This is funny because a little snow never hurt anyone, except for maybe crops, but Scout takes it for the worst possible event because it is new and unfamiliar to her. Fortunately, as Scout progresses, grows and matures, she starts to use her brains to figure things out rather than listening to superstitious tales.