Are Hogwarts students allowed to do magic over the Christmas/Easter holidays?

Question

The Hogwarts staff go out of their way to impress upon students that doing magic during the summer holidays is forbidden, even going so far as issuing notes.

...notes were handed out to all students, warning them not to use magic over the [summer] holidays (“I always hope they’ll forget to give us these,” said Fred Weasley sadly)...
_{(Philosopher's Stone, Chapter 17, The Man With Two Faces).}

The Ministry takes underage wizardry very seriously. They seem happy to expel people (or Harry, at least) after just two infringements. Yet the vast majority of students go home to spend Christmas with their families (the exception was in Goblet of Fire when everyone wanted to stay for the Yule Ball). There are also the less-mentioned Easter holidays.

“My son, Draco, is home for his Easter holidays. If that is Harry Potter, he will know.”
_{(Deathly Hallows, Chapter 23, Malfoy Manor).}

I don't recall any mention of any ban on doing magic outside school during either the Christmas or the Easter holidays. This seems inconsistent. Is magic at home forbidden during those holidays too? Is there some indication that the teachers did instruct students not to do magic that I missed?

Answer 1

The reasonable restriction for underaged sorcery bans all magic by underaged wizards outside of school, (regardless of which holiday it is). This is made clear by Mafalda Hopkirk in CoS, when she sends a letter to Harry for his use of the Hover charm.

'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).' (Page 21 Chamber of Secrets)

This means that anytime that a wizard or witch uses magic, while underage, outside of school it is technically illegal. However, while discussing Voldemort killing his father and blaming Morfin however Harry gets upset, saying that the ministry should have known because Voldemort still had the trace, at which point Dumbledore explains that the trace can detect magic in an (unspecified) area around underaged wizards, but not the caster. Remembering that Harry was blamed for the hover charm that Dobby cast, because he was the only wizard within several blocks of the spell.

He continues to say that non-muggle, young wizards would be able to use magic without the ministry knowing, because the ministry would assume the parents did the magic, therefore it is the parents job to uphold the rules of 'no underaged magic'.

Additional reading about the Reasonable Restriction of Underaged Sorcery: Decree for the Reasonable Restriction of Underage Sorcery.

Edit: Reorganized for clarity in concern to the question.

Answer 2

In Harry Potter and the Half-Blood Prince, Ron and Harry are at the Burrow for the Christmas break. They have to peel sprouts by hand as they are unable to use magic. Ron complains that he is only 2 1/2 months from being able to use magic outside of school. Ron tries to convince Fred and George to finish them by magic for them as they are 'of age'.

“I’ll be seventeen in two and a bit months’ time,” said Ron grumpily, “and then I’ll be able to do it by magic!”

(Half Blood Prince, Chapter 16: A Very Frosty Christmas, The Burrow)

Answer 3

They aren't allowed to do magic.

As Grizzy Jeff points out, we see in book six that they are forbidden to use magic during the Easter Holidays as well

"Aaah, George, look at this. They're using knives and everything. Bless them."

"I'll be seventeen in two and a bit months' time," said Ron grumpily, "and then I'll be able to do it by magic!"
_{Harry Potter and the Half-Blood Prince - Chapter Sixteen}

The reason why Harry doesn't notice (or alternatively, Rowling doesn't mention) the notes being handed out until the summer holidays is because Harry wasn't going home before then.

“I do feel so sorry,” said Draco Malfoy, one Potions class, “for all those people who have to stay at Hogwarts for Christmas because they’re not wanted at home.”
_{Harry Potter and the Philosopher's Stone - Chapter Twelve}

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Tl;dr: You can feel free to go after Harry any time he isn't at Hogwarts.

Answer 4

If they stay at Hogwarts - yes. Guess, in their magical families as well. However, if they are outside, the rules for the summer vacation are still applicable mostly because they all live with muggles.