Well, superficially, I think the sentence is illogical. Since" each and every day of the year"= "every day of the year", is it possible for one to hold exhibitions every day? (Or possible, if the organiser is rich enough.)
Throughout means during all of the year.
Perhaps, you may rephrase the sentence as follows if exhibitions are not run every day of the year:
We conducted educational exhibtions at the weekends throughout the year.
Student or Learner