I think the word for 'study season' is .
In most Japanese elementary and middle schools, there are three in one school year. 1 starts in April and ends in mid July (with Golden Week in May), followed by (summer vacation). 2 starts in September and ends in December, followed by (winter vacation). 3 is a relatively short from January to March. There's (spring vacation) before the next school year begins, lasting for a few weeks. There are some schools which have irregular systems, but they are called anyway.
The generic term for long vacations is or , but these sound stiff and technical. In conversations we just say , , etc.