Time of year refers to natural divisions of the year based on seasons (spring, summer,) or other natural changes (equinoxes, solstices). I suppose it's more of an expression. The preposition 'at' is used in the expression, "at any time of year"
Example: Strawberries are cheap at any time of year. (meaning either in April or Summer, Winter, Christmas) or Typhoons occur at any time of year. (either January to Feb or November to December
The idea of using 'at' is it is fixed--a specific time.
We use it with holidays.
At New Year's Eve