PROBLEM WITH YOUR CODE:
the function will be called when you refresh, because on refresh the page is unloaded and then reloaded.
in your solution, you should also note that you are not assigning a function to window.onbeforeunload but you are assigning the return value of the function when you write
window.onbeforeunload = confirmWinClose();
which might also execute the function (based on where you place it in the javascript) whenever the assignment is done. For e.g. 
function confirmWinClose() {
var confirmClose = confirm('Close?');
return confirmClose;
}
window.onbeforeunload = confirmWinClose();
the above code will execute the confirmWinClose function whenever this js is loaded.
(not your case as you have defined the function after call, so won't be executed on load, but you should remember this)
SOLUTION:
the below solution is working for close also
instead of your solution, i tried this
JS:
window.onbeforeunload = function() {
    var confirmClose = confirm('Close?');
    return confirmClose;
}
or 
 window.onbeforeunload = confirmWinClose; //note the absence of calling parantheses
    function confirmWinClose() {
        var confirmClose = confirm('Close?');
        return confirmClose;
    }
this works as expected.
also note that you should return from the onbeforeunload explicitly. 
even if you have to call a function, you should do
<script>
    window.onbeforeunload = function(e) {
       callSomeFunction();
       return null;
    };
</script>