Nos livros, parece que o verão antes de começar Hogwarts.
As cartas de Hogwarts de Harry começam a chegar antes de seu aniversário - os Dursleys tiveram tempo de trocar de quarto, ir a um hotel e se esconder em uma cabana, tentando se esconder das cartas. O aniversário de Harry acabou sendo o prazo para responder, quando Hagrid teve que cuidar de Harry.
*“Dear Mr Potter,
We are pleased to inform you that you have a place at Hogwarts School of Witchcraft and Wizardry. Please find enclosed a list of all necessary books and equipment.
Term begins on 1 September. We await your owl by no later than 31 July.”*
- Harry Potter and the Philosopher's Stone, Chapter 4 (The Keeper of the Keys)
Assim que Hagrid o encontra, ele envia uma resposta para a coruja.
“With his tongue between his teeth he scribbled a note which Harry could read upside-down:
Dear Mr Dumbledore,
Given Harry his letter. Taking him to buy his things tomorrow.
Weather’s horrible. Hope you’re well.
Hagrid”
- Harry Potter and the Philosopher's Stone, Chapter 4 (The Keeper of the Keys)
Portanto, nos livros, o prazo parece coincidentemente coincidir com o aniversário de Harry.
No entanto, um texto sobre Pottermore diz que é o décimo primeiro aniversário deles.
De acordo com o artigo sobre Minerva McGonagall publicado no Pottermore, a carta dela veio no dia do seu aniversário.
Minerva never forgot how much her mother cried, when the letter of admittance into Hogwarts School of Witchcraft and Wizardry arrived on Minerva’s eleventh birthday; she knew that Isobel was sobbing, not only out of pride, but also out of envy.
Minerva McGonagall (Pottermore)
Isso não faz muito sentido pelo motivo declarado na pergunta.