Yes, they are.
The ban on doing magic during the holidays basically means that underage witches and wizards can't do magic outside Hogwarts. Doing magic at Hogwarts is fine at any time of the year.
The purpose of the restriction is basically twofold.
- To prevent students from doing magic in front of Muggles and breaking the Statute of Secrecy.
- To stop unqualified kids from doing magic that may be dangerous or beyond their abilities without the presence of a responsible teacher to look after (/punish) them.
On the first point, Hogwarts is far away from any Muggles so students can do as much magic as they want there without breaking the Statute of Secrecy. On the second, there are obviously plenty of teachers on hand even during the holidays (they seem to stay there the whole year round) so unsupervised magic isn't a problem either.
Essentially, it makes no more sense to put restrictions on kids doing magic at Hogwarts during the holidays than it does at any other time of the year. It's a magical school; the kids are kind of there to do magic so there's no point in stopping them. Any ban on doing magic during the holidays would probably be impossible to police anyway.
Additionally, it's worth noting that exams follow fast on the heels of the Easter holidays. Those holidays are widely used for revising and studying for those exams, as well as for catching up on homework. Banning magic during this period would seriously hinder the ability of students to perform at their best in important exams.
From the books we know that students do perform magic during the holidays. I've beefed up this section to try and meet the criteria that @Anthony Grist suggests in the comments - namely, a student doing magic in front of a teacher during the holidays in such a way that they would be reprimanded when caught. No such clear-cut example exists. I've combed the books for examples and, even if students weren't necessarily doing magic in front of the teachers, it's pretty clear to my mind that they were doing magic, in private at least. We have several examples.
Hermione whipped up a Sleeping Draught during the Christmas holidays and no action was taken against her.
“I’ve got it all worked out,” she went on smoothly, ignoring Harry’s and Ron’s stupefied faces. She held up two plump chocolate cakes. “I’ve filled these with a simple Sleeping Draught. All you have to do is make sure Crabbe and Goyle find them."
(Chamber of Secrets, Chapter 12, The Polyjuice Potion).
Ron also performs a Severing Charm during his preparations for the Yule Ball during the Christmas holidays.
In a desperate attempt to make them look more manly, he used a Severing Charm on the ruff and cuffs. It worked fairly well; at least he was now lace-free, although he hadn’t done a very neat job...
(Goblet of Fire, Chapter 23, The Yule Ball).
With thanks to Au101 we also have the example of kids doing duelling during the holidays.
...he, Hermione, and the Weasleys had the run of Gryffindor Tower, which meant they could play Exploding Snap loudly without bothering anyone, and practice dueling in private.
(Chamber of Secrets, Chapter 12, The Polyjuice Potion).
During his first Christmas holidays Harry lights up a lamp in the library.
The library was pitch-black and very eerie. Harry lit a lamp to see his way along the rows of books.
(Philosopher's Stone, Chapter 12, The Mirror of Erised).
You could argue that this was done non-magically but then again we do have examples of him lighting lamps by magic from another book.
It was dark and empty when he arrived, but he lit the lamps with his wand...
(Prisoner of Azkaban, Chapter 12, The Patronus).
The most clear-cut example we have (or the one that comes closest to magic done in front of teachers) is Fred bewitching Percy's prefect badge.
Percy, who hadn’t noticed that Fred had bewitched his prefect badge so that it now read “Pin-head,” kept asking them all what they were sniggering at.
(Chamber of Secrets, Chapter 12, The Polyjuice Potion).
Whether he did it in the Great Hall in front of the teachers or not is perhaps debatable. But since Percy takes such pride in his appearance (and in his badge above all) I think we can say that it hadn't been bewitched for very long at this point. So the bewitching charm was definitely done in the holidays. Quite possibly, it was done during lunch in the Great Hall in front of the teachers.
In short, every indication is that underage magic continues apace during the holidays. There is no attempt to stop or curtail it by the teachers. If it is forbidden then that ban is certainly not enforced.
The quote in the question also confirms that it's magic done outside school which the Ministry is concerned with.