Os estudantes usam roupas trouxas enquanto não estão em aulas em Hogwarts (como fazem nos filmes)?

Não, basicamente nunca em Hogwarts. Na cena em O Prisioneiro de Azkaban que você tem uma foto na questão, por exemplo, eles estavam usando mantos. Por exemplo, depois que tudo aconteceu e eles estão na ala hospitalar e Dumbledore sugere que eles deveriam usar o Time-Turner, nós temos:

But Hermione was fumbling with the neck of her robes, pulling from beneath them a very long, very fine gold chain.

Harry Potter and the Prisoner of Azkaban - p.288 - Bloomsbury - Chapter 21, Hermione's Secret

Quando vão a Hogsmeade nos finais de semana, eles vestem roupas. Por exemplo, isso foi logo depois que Harry voltou de Hogsmeade, quando ele jogou lama em Malfoy, Crabbe e Goyle e Malfoy viu sua cabeça em Hogsmeade quando seu manto de invisibilidade caiu:

Harry followed him downstairs, trying to wipe his hands clean on the inside of his robes without Snape noticing.

Harry Potter and the Prisoner of Azkaban - p.208 - Bloomsbury - Chapter 14, Snape's Grudge

Também os vemos usando vestes durante as reuniões do DA, à noite depois da escola (embora também estejam uniformizados para os encontros do DA nos filmes):

'Well, my dad is very supporting of any anti-Ministry action!' said Luna Lovegood proudly from just behind Harry; evidently she had been eavesdropping on his conversation while Justin Finch-Fletchley attempted to disentangle himself from the robes that had flown up over his head.

Harry Potter and the Order of the Phoenix - p.350 - Bloomsbury - Chapter 18, Dumbledore's Army

E durante os fins de semana. Eles vão ver Grope durante a partida final de quadribol da temporada, que é no último fim de semana de maio. Enquanto eles caminham pela floresta:

It was a great struggle to keep up with Hagrid, what with branches and thickets of thorn through which Hagrid marched as easily as if they were cobwebs, but which snagged Harry and Hermione's robes, frequently entangling them so severely that they had to stop for minutes at a time to free themselves.

Harry Potter and the Order of the Phoenix - p.606 - Bloomsbury - Chapter 30, Grawp

Também usam roupas no Natal. Eles levaram a poção Polyjuice no dia de Natal:

His shoulders stretched painfully and a prickling on his forehead told him that hair was creeping down towards his eyebrows; his robes ripped as his chest expanded like a barrel bursting its hoops; his feet were agony in shoes four sizes too small ...

Harry Potter and the Chamber of Secrets - p.162 - Bloomsbury - Chapter 12, The Polyjuice Potion

Em A Pedra Filosofal eles ainda usavam túnicas para a maior parte da viagem para casa no Expresso de Hogwarts:

And suddenly, their wardrobes were empty, their trunks were packed, Neville's toad was found lurking in a corner of the toilets; 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); Hagrid was there to take them down to the fleet of boats that sailed across the lake; they were boarding the Hogwarts Express; talking and laughing as the countryside became greener and tidier; eating Bertie Bott's Every-Flavour Beans as they sped past Muggle towns; pulling off their wizard robes and putting on jackets and coats; pulling into platform nine and three-quarters at King's Cross Station.

Harry Potter and the Philosopher's Stone - p.222 - Bloomsbury - Chapter 17, The Man with Two Faces

Na verdade, Harry está tão acostumado a usar túnicas, nós deixamos isso de lado no St Mungo's, onde eles usavam roupas trouxas para se misturarem na viagem para Londres:

(Harry wanted to stamp on Ron's foot, but that sort of thing is much harder to bring off unnoticed when you're wearing jeans rather than robes.)

Harry Potter and the Order of the Phoenix - p.454 - Bloomsbury - Chapter 23, Christmas on the Closed Ward

Este é um dos meus pet ódios sobre a franquia de filmes, como acontece. Arruina a imersão.

Eles fazem , no entanto, usam pijamas na cama.

Sim, sim, pelo menos os Weasleys.

Harry felt a slight sense of foreboding. He had rarely seen Mr or Mrs Weasley wearing anything that the Dursleys would call ‘normal’. Their children might don Muggle clothing during the holidays, but Mr and Mrs Weasley usually wore long robes in varying states of shabbiness. Harry wasn’t bothered about what the neighbours would think, but he was anxious about how rude the Dursleys might be to the Weasleys if they turned up looking like their worst idea of wizards. -Goblet of fire

Mais uma vez, os Weasleys, mas no Natal, eles usam jeans, o suéter que sua mãe faz deles

‘Hey, look – Harry’s got a Weasley jumper, too!’ Fred and George were wearing blue jumpers, one with a large yellow F on it, the other with a large yellow G.

They frog-marched Percy from the room, his arms pinned to his sides by his jumper.

A primeira vez, nos filmes, que vemos estudantes usando roupas não uniformes, dentro de Hogwarts, está no primeiro filme, Harry Potter e o Pedra Filosofal (2001) , embora pareça ser apenas durante as férias de Natal, fora das aulas, durante o tempo livre.

De acordo com o wiki , isso também é verdade nos livros, e eles dão 3 exemplos:

In the films, students wear normal Muggle clothing on their free time or outside of their lessons. This appears to be true in the books as well. Ron Weasley and his siblings typically receive sweaters from Mrs Weasley as Christmas presents, despite still having six more months of school left. In the sixth book, Draco Malfoy shops for new robes even though the school year is about to begin. Also in the sixth book, Lavender Brown asks Harry about Ron's - her boyfriend at the time - true opinion of her new dress robes.

Não é até a terceira parcela da franquia de filmes, Harry Potter e o Prisioneiro de Azkaban (2004) , que os vemos usando roupas não uniformes quase o tempo todo (fora das aulas, comendo no salão etc.), como você mostrou na foto.

Isso certamente parece se desviar dos livros, onde os alunos são obrigados a usar suas vestes uniformes, como outras respostas demonstraram.

O diretor do filme, Alfonso Cuarón , fez essa escolha de design, afastando-se dos livros, conscientemente.

Alfonso Cuarón had the idea to have Harry, Ron, and Hermione wear everyday clothes more often than their Hogwarts uniforms in order to show more of the characters' personalities. He also gave the rest of the Hogwarts students permission to wear their uniforms any way they wanted to in order to bring a greater sense of realism to the wizards' school, hence why some of the students wear the uniforms very neatly while others have the shirts and ties hanging out.
^{_{- IMDB trivia (source)}}

Em uma das entrevistas nos recursos de bônus do DVD, Cuarón fala sobre como as crianças estão mais velhas agora, o bicho-papão não mora mais no seu closet, mora dentro deles, então ele queria trazer uma sensação muito naturalista para a performance e a escrita das crianças, dizendo que os uniformes maltratados e as roupas não-uniformes (trouxas) ajudavam a trazer esse nível de realismo e individualismo que ele sentia que acrescentaria ao naturalismo que ele queria acrescentar.