Y'all are making this harder than it has to be. I sure as heck don't soak it overnight!
When I'm measuring out the beet pulp rations, I put them in the horses' feed pans dry, along with their other feed.
I have a bucket of hot water, and add enough water to each feed pan to completely cover the feed/beet pulp mixture.
It takes about 5 minutes for the feed/beet pulp to soak up the water. Once the water's soaked up, I stir the mixture with a wooden spoon to break up any clumps, then give it to the horses.
Really, there's no reason to soak beet pulp overnight unless you have an IR/Cushings horse, and the beet pulp needs to be drained before it's fed.