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At the very end of Philosopher's Stone we are told the following:

notes were handed out to all students, warning them not to use magic over the holidays ("I always hope they'll forget to give us these," said Fred Weasley sadly);

This makes it seem like not giving out the notes would have made some sort of difference. However, that should not be the case. Underage wizards using magic outside of school is not (merely) a violation of a school rule; it's a violation of the law. As we find out from Mafalda Hopkirk in Chapter Two of Chamber of Secrets:

As you know, underage wizards are not permitted to perform spells outside school, and further spellwork on your part may lead to expulsion from said school (Decree for the Reasonable Restriction of Underage Sorcery, 1875, Paragraph C).

Given that this is an actual law, using magic would be a violation of the law whether or not the school happened to send home a reminder. So Fred's hope seems misplaced. Even if the school forgot to give them the notes he still wouldn't be allowed to do magic.

Now it is possible that the notes are for the benefit of the parents/guardians, with the point being to remind them to keep an eye on their underage children. However, that hardly seems useful. A student could simply not give the note to his/her parents/guardian. Indeed that seems to be exactly what Harry did:

"Oh, I will," said Harry, and they were surprised at the grin that was spreading over his face. "They don't know we're not allowed to use magic at home. I'm going to have a lot of fun with Dudley this summer...."

Moreover, the law against underage magic seems to be sufficiently well-known that wizarding families wouldn't suddenly forget about it just because they didn't get a reminder from Hogwarts. If Mrs. Weasley caught Fred doing magic I highly doubt she would be swayed by his argument that the school didn't send home any notes that year.

Is there some other purpose that the notes serve such that Fred would not want them to be given out? Otherwise, why does he care?

If the notes are not given out, then presumably Fred could conceivably claim that they were not made aware of the rule. In that case, they would not be at fault for doing magic, because they can blame the school for not telling them. Also, if they consistently give out these reminders, and then one year do not, then it's perfectly reasonable to think that it no longer applies.

In any case, if the school did not give them these notes, then Fred could in theory claim that he was not made aware of the rule / thought that it no longer applied, because the school did not carry through on its requirement to let them know about it. Fred, being Fred, would be able to wreak some minor havoc using magic, and then finagle his way out of trouble by blaming the school.