Checking/Unchecking check box array with jQuery

I have a HTML form with check boxes of seasons, and set of buttons of seasons. I want jQuery to select check boxes when I click on the buttons. For example when I click on the Winter button it should check the Dec,Jan, Feb check boxes. Somehow my code does not seems to work.

$("#btnWinter").click(function() {
  $("#season[0]").prop('checked', true);

});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
Season <label><input type="checkbox" id="season[]" name="season[]" value="January"> January </label>
<label><input type="checkbox" id="season[]" name="season[]" value="February"> February </label>
<label><input type="checkbox" id="season[]" name="season[]" value="March"> March </label>
<label><input type="checkbox" id="season[]" name="season[]" value="April"> April </label>
<label><input type="checkbox" id="season[]" name="season[]" value="May"> May </label>
<label><input type="checkbox" id="season[]" name="season[]" value="June"> June </label><br/>
<label><input type="checkbox" id="season[]" name="season[]" value="July"> July </label>
<label><input type="checkbox" id="season[]" name="season[]" value="August"> August </label>
<label><input type="checkbox" id="season[]" name="season[]" value="September"> September </label>
<label><input type="checkbox" id="season[]" name="season[]" value="October"> October </label>
<label><input type="checkbox" id="season[]" name="season[]" value="November"> November </label>
<label><input type="checkbox" id="season[]" name="season[]" value="December"> December      </label><br/>

<input type="button" id="btnWinter" name="btnWinter" value="Winter" />