What is it like to be a debater in a law school? Do debaters read from their prepared manuscripts?

I am assuming you are talking about American law schools, and you are talking about either Moot Court, or mock trials, or a NITA-style class. NITA = National Institute for Trial Advocacy.

The answer is that it depends on the comfort level of the speaker with the material. When I was in law school, they taught us a card method for keeping your points at the forefront of your mind, and I hated it. I also took a Product Liability class where we conducted a mock trial. I gave the closing argument for one of the three defendants; my two classmates gave the closings for the other two defendants, plus someone gave closing for the plaintiff. I had a written outline I had created. I did not read from it, but it had the main points I wanted to make. My classmates in defense both shot from the hip and spoke extemporaneously.

I won my case; they didn't.

So preparation mattered there, but I might just have been more persuasive.

Oh, and don't call them manuscripts. A manuscript is a handwritten document or an author's text prior to publication. The more accurate term you're looking for is probably notes or outline. Writing out and then reading aloud a full-fledged closing argument is generally a poor idea, as there is very little eye contact with the fact finders and it can seem rather dull. Plus, if permitted to do so by the judge, many lawyers move around, rather than stand at a podium when it comes time for closing arguments.