He he he... it will be wet in places! I have run this course in ordinary road shoes/trainers, but it seems that most people enjoy a little bit more grip. The terrain is mostly sandy tracks, and is generally well-drained, but there are likely to be some monstrous and near-impassable puddles.
I'd wear trail shoes if you have 'em, but I'd still be happy enough to run this in trainers.
Why just watch the Wife Carrying? ... it's only 250m! C'mon!