At (among other uses) is used for weekends, public and religious holidays, meal times, and times of day. For example: at the weekend (BrEng usage); at Christmas and at Easter; at lunch; and at 12 o'clock.
Holiday breaks usually consist of more than one day, so when you refer to Christmas you are thinking about Christmas eve, Christmas day and Boxing day (also called ‘St.Stephen's Day’). The Easter holiday is usually made up of two days; Easter Sunday and Easter Monday. N.B. Good Friday is not a public holiday in Italy but it is in the UK.
Thus the question should read:
Did you have a good time at Easter?
On is used in the following: on the weekend (AmEng), on Christmas day and on Easter Sunday. The preposition on is normally used for dates (i.e. on 25th December) and days of the week. In British English, people ‘go on holiday’ but in American English they ‘go on vacation’.
In is normally used with ‘weeks’, ‘months’ and ‘years’, for example: in two two weeks' time; in July; and in 2016.
Because the OP's sentence uses the plural noun form, holidays, and the choice is limited to at/in/on, I suggest that in is the most appropriate preposition.
I'll call her in the holidays.
In a multiple-choice test paper, a student's answer which completely ignores the options, will always be marked incorrect. Regardless if the given answer is an improvement, e.g. "during" and "over" as suggested by @AleksandrH
Comparing on the summer holidays and in the summer holidays the British English corpus seems to agree that in is idiomatic and grammatical, and doesn't find any instance of the former. Ngram link
Meanwhile the American English corpus shows the occurrences of on the summer vacation (red line) as being exceptionally rare, compared with in the summer vacation (blue line) and in the summer holidays (green line).
For more detail see
"On/at/for/over the weekend" in American English
"On the weekend" or "during the weekend"
Is there a difference between "holiday" and "vacation"?
Holidays or holiday?
"next two weeks" vs. "in 14 days from now"