I study software engineering, so not true computer science but a computer science related degree. All degrees will have you write at least some kind of essay, be it individual or in a group. Throughout my first year I've written two essays that I can recall. One was more a pre-arrival activity where you basically stated why you chose to go to that particular uni, etc (although we were graded on it and it does contribute a very small amount to our first year grade). IIRC there was a purposeful low word limit on it (~1000 words) to make you spend equal amounts of words on each section and not overrun. The second was a group essay, I think a group of 6 of us had to write a ~3000 word essay (again, purposefully low word count) about how the job requirements have changed/will change in an area of computing from a given list (we did computer security). So yeah... two essays. You will most likely get given many more coursework based assignments such as programming activities, for example. I think we've had 13 marked programming assignments to do and many more unmarked, as well as online tests for networking & databases, a presentation we had to give, a systems analysis group excercise, and a databases assignment which we finished at 02:00 monday morning (with time to spare for the 09:00 deadline). Then in the summer we have our proper exams, yay!
Apologies for no paragraphs/poor structure, I didn't intend to go on for that long. If you have any questions, feel free to ask.