Heater core issue?
If you want to be sure just disconnect the two hoses that run to the heater core and block them off. Blow out the heater core with an air compressor to remove any coolant..put a hose on one side and route it to a drain pan.....be careful.
Now block off those two hoses with something and see if you get anymore haze from your defroster. If not then you have a bad core.
I also agree that you probably have a bad core but it never hurts to do an easy check before you commit to the hard work.
Good luck. :D