Cutting off the end of the hose may help but the hose can be plugged all the way back. Find a full service station and ask then to blow out the air conditioner drain line.
They'll use compressed air, and if thats the problem it will be solved.
On a side note, every Impala I ever owned, or saw, had a windshield that leaked (eventually). but I havent owned one since 1986 model.