I think Tough Mudder exists just so that those who've done Tough Guy can laugh at people in the pub who claim Tough Mudder is 'hard'. If you're going to do something like this, do the real deal, and get to Tough Guy.
Done it three times, and as others have probably told you, its the cold that's the killer. It's not actually all that far, so masses of fitness isn't needed...but...the faster you get round the quicker you're out of the cold. It's one of the very few events where instead of giving the advice 'pace yourself', I'd be more inclinded to say 'run like hell right from the start!' The reason I say this is that once you get to the 'killing fields' you haven't got a lot of running left to do, but will face some serious cold endurance. Last year was quite mild and not so bad, but get a sub-zero year and it's this bit that makes it 'tough'. ( Much harder than all the usual 'mud races' ). Good luck, it's a superb event, by far the best I've ever been involved in, atmosphere is something else.
Done it three times (last 3 years), and doing 2013 too. Only ever in normal running shorts and vest. I can't therefore comment on other suggestions, but nothing has made me want to try any other type of clothing because TBH the cold only kicks in as a serious problem *after* you're soaking wet, so anything thick and heavy will do virtually nothing useful prior to the water and be an absolute nightmare afterwards. I have nothing but respect for the lunatics who try it in fancy dress, but it must be horrific (the big stuff that is - those who run virtually naked are probably no worse off than anyone else). Obviously neoprene would be a different matter, but then I kind of think that's not the Tough Guy 'spirit' - the event isn't really intended to be something a bit like a triathalon - it's all *about* the extreme conditions, rather than trying to avoid them.
The biggest mistake I made the first time (and never again!) was to not arrange quick access to a towel and lots of thick dry clothes after the race. My bag was with a friend and I was semi-hypothermic trying to find them for about 15 minutes - the worst part of the day by far! Pack a bag with lots of warm clothes and make an accurate mental note of exactly where you left it, rather than leaving it with a friend - it's so busy and maze-like around the finish you might not find each other quickly.
Fingerless gloves are essential for the ropes, but you can buy these on the day.