If they offer you a wetsuit and booties wear them, if I were on a paddle boat and wanted to be in the front where the action is, I'd ask for them. If its clouding up, a splash top will also be nice to have.
Some of the water on Brown's will have been frozen a couple of days before and all of it comes from high altitude reservoirs where its still pretty chilly. The river is great for cooling your beers down to a good temperature for drinking. If you're overdressed for the run, its easy enough to cool down by splashing yourself. If you're cold, you'll be cold until the takeout unless they stop and build a fire because people are hypothermic.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse