2003 Ford F150 Engine missing

Last week, I slid off the road during a snowstorm. I was picked up, and later came back to get my truck pulled back onto the road. I had mistakenly left the headlights on when I was rescued, so we had to jump the truck off. When I raised the hood, I saw that the wind had blown quite a bit of snow thru the grill and under the hood and was now covering the engine. The truck started fine with cables and I drove the 4 miles into town with no problems. However, when i went to start the truck again the later, it was running rough, seeming to miss. When I put it in drive, it got worse, finally dying altogether. I could start it back up, with it still missing a little, but again when I put it in drive, it would sputter and finally stall out. I am thinking that the snow melted with the heat of the running engine and may have gotten into something, but I don't know what to check. How do I diagnose where the problem is, and how do I fix it?
Thanks.