Well, pretty much as described... I went to the Nexus page > Frostfall > Description > Troubleshooting. Chesko has provided three possible solutions to the script error problem there. As far as I understand it, you tell Skyrim to give more memory to the scripting system by editing your Papyrus log (which can be found in /my Games/Skyrim/Skyrim.ini).
Open up that file, make a copy first so you can undo if necessary, and where you see Papyrus mentioned add the lines that Chesko provided, or change the values if the same line of code is already present in your log. Save and play Skyrim to see the results.
As I said, I had to try all three solutions provided. The first didn't help, the second reduced my framerate to a gibbering wreck, but the third worked splendidly. I must also say, I knew the problem couldn't be down to my own computer seeing as it's brand new and rather powerful (I call it my Beast).
I hope that helps. This feels very weird, your know, telling others what to do as I have not a single idea how all this works myself! If a more knowledgable person notices that I said anything wrong, please correct me!