Generally, I think even slow typers are able to finish their tests without a problem, so typing speed probably won't be a deal breaker on most tests. However, some tests, like my torts exam and its absurd amount of issues, basically turn into typing contests where you can almost rank everyone's grades by their typing speeds.
Where I think typing speed matters most is in note taking. I type pretty fast and still sometimes miss stuff. Even if you take really concise notes, the parts worth writing usually come in chunks that are easy to miss parts of. And then you have the occasional professor that basically wants you to write everything they said over the course of the semester on the test, which means you'll be wanting to literally write down almost everything they say.