Did I do any damage to my car?

Last night my friend and I were driving and the low coolant light came on in my car. At the time I didn't know what that meant, so I shut off the A/C and opened the windows. We continued driving. I didn't see any smoke or smell anything out of the ordinary. We passed her house and I tried to find a street in which to make a K turn so that I was facing in the right direction to drive home after dropping her off.

We turned up this long, uphill, narrow, dead end road, and finally reached the end, where I tried to do the K turn. It was really steep and because we were angled downhill we almost rolled into a ditch when I shifted from reverse to drive. I floored it and the tires screeched, pulling us out of the ditch and back onto the road. That's when I noticed that there was smoke coming up from under the hood and it started to smell like something was burning. The smoke and smell dissipated as we continued driving but I did not notice any smoke or smell until that point, as the windows had been open. I checked the temperature on the dash and the bar was between H and C so the car was not overheated. I drove her home, parked the car, and had her stepdad pop open the hood and take a look.  It appeared to be leaking coolant and radiator fluid, not oil.  When I maneuvered the car to get it further off the street it was still leaking on the pavement.

The car was towed on a flatbed and when it rolled off the flatbed there was leaked coolant on the flatbed, leading me to believe that it was leaking all that time and that I didn't overheat or do any damage to the engine or the heating core. I think that the water pump gave way, which caused the coolant and radiator to leak.

I hope that it just has to be flushed and some hoses replaced. I couldn't have driven more than 8 miles with the "Low Coolant" light on. Did I do any severe damage to the engine or heating core of my car?  Did I seize the engine or blow a gasket or is this an easy fix?