Ok, I'm getting some links for you...
This one is from http://distanceriding.org/index2.php...do_pdf=1&id=35
It's long, so I copied and pasted the parts relevant to this conversation. While it does say it's unnecessary to soak beet pulp, it points out that horses will generally drink enough water to properly digest it. However, it doesn't address when horses aren't drinking enough water, as seemed to be your case. It also says it often takes 3-4 hours to soak beet pulp, which is what I've found with my horses. Here's the quote:
Assuming free access to water, horses will voluntarily drink
enough water to adequately process any amount of beet pulp consumed (1.5 to 2 litres per pound of beet pulp).
Although soaking beet pulp is not necessary,
there are several good reasons for wetting it down before you feed it. Soaking beet pulp may make the feed easier to chew, particularly for older horses with bad teeth. Soaked beet pulp may also be more tasty and it provides a useful method for hiding minerals or medications. If your horse gobbles down his feed or is prone to choke, it might be a good
idea to soak your beet pulp. And while horses will drink water on their own, pre-soaked beet pulp is a good way to get
some water into your horses, particularly in the winter when they may not be as inclined to drink what they need. So, if
soaking beet pulp fits into your feeding management, by all means, do it. You don't have to soak beet pulp overnightmost of the expansion takes place within the first 3 to 4 hours.