Great letter! It's 'the' because there is only one Chinese summer conceptually speaking (yes, there's one every year, but in general terms). Your son correctly refers to 'the Australian winter' for the same reason. (We can say both 'in summer' and 'in the summer' but 'the Chinese summer' is more specific.) 'There's a long time from now until the summer holidays.' (Capital T; 'from'; personally I'd say 'holidays' in the plural) Anyway,' (comma) Capital T for 'That's my cool news'. (I assume there is an 's' on the end of 'news', as it's not quite visible.) 'What do you think?' (question mark) Also, I don't know how strict your son's teachers are about starting sentences with conjunctions like 'And' given that this is an informal letter, so you might want to check that. There are what look like full stops before some 'but's, but maybe they are commas (as they should be).

Hi, that is because he's not writing about summer in general, but specifically about the summer in China. Another example: Are you familiar with Bryan Adams' song, Summer of '69? If you listen to his lyrics, you will hear that he is not singing about just any summer, but about a specific summer: the summer of 1969.