Leaving wet is said to create heat, body warms the water and they stay warmer longer.
We would leave the belly damp, but blow most the water out off the body, then put in front of fans with their morning feed and let them dry completely.
As stated you run into hair training problems by leaving them wet, and if they are tied wet and lay down it is bad as well.
Here is what I would suggest, rinse, scrape excess water off, comb, tie and feed, do the rest of your morning chores, get ready for school. Come back and use a double blower to blow rest of the water out, probably will take 5 to 10 minutes per animal to get them dry enough. We have what they call May Gray and June Gloom, (foggy mornings) we could never get them completely dry in the morning, but we got the water off them and the hair was up. and the skin was damp to the touch but no water standing or wet areas. We fed them then and let the fans blow the dry the rest of the way. In the evening they are blown out completely and the hair worked after rinsing and again before they get kicked out at night.
There are allot of routines, you have to find one that works for you and still promotes optimum hair growth, you may need to start one routine and modify it until you find a routine that works for you.