Here's your likely solution. (when it finally warms up) Remove the wiper arms and open the cowl (with the hood open you will see the screws) and then clean out all the leaves and junk that you can on either side. Next, put a light inside the cowl and if you look through the gap behind the fender when the door is open you should see light from the drain holes. If not, they are clogged with crud and you should poke them clear with a coat hanger or something.
After that, remove the vent covers on either side and pull out all the leaves and stuff stuck in there (I lubed the cables while I was at it. Someone had taken mine apart before and assembled it wrong so one side wouldn't open and the other wouldn't close!). I'd wear gloves because I found sharp stuff in there!
Mine was partially rusted in there, so I poked out the bottom to make sure no more water can build up.