Loosie, any type of feed that a horse gorges himself on can cause problems. However, beet pulp has been PROVEN, by vet school studies, NOT to swell in a horse's stomach or esophagus when fed dry. In a few different studies, horses were fed up to 50% of their daily forage intake with beet pulp in its two different forms, pelleted and shredded, DRY and NONE of the horses had any signs of colic or digestive upset.
A horse's stomache can hold approximately 5-7 lbs of hard feed at any one time (10 qts, I think). It only takes 15-20 minutes for that food to be processed out of the stomach.
Now, if the horse bolts his feed down or can't/won't chew properly, then choke can be a concern. But, choke would be a concern with ANY kind of hard feed (grain, pellets, textured) or hay cubes.
Feeding beet pulp wet or dry, for most horses, is simply personal preference for the owner and the horse. Some horses prefer it wet, some prefer it dry. Some owners don't want to risk choke or need it wet to mix in supplements. Some prefer the ease of mixing it dry in to other grains or feeds. It's all up to the owner to choose, wet or dry.