Is it possible to get a list of everyone who graduated from a college in a given year/field? I am interested in doing a project on graduate life-paths and need to be able to see the cohort a student graduated in in a given subject?

i.e. can I say I want a list of all the people who graduated from College College in 19XX with a BSc in Television Television?

So I have been googling and just started writing to schools, but I've been unable to find this or find out if it is even possible to gain access to such a database.

I appreciate your help and look forward to your thoughts!
Such data exists at the universities and departments. However, in many jurisdictions there are legal restrictions that would limit their ability to share it with you. There are also practical limitations: the departments want to keep a good relationship with their alumni. If the alumni get contacted every other week by someone doing a project, then that would be bad. 

So to get access to these data is hard work. You need to convince them that this is a serious project, maybe you need IRB approval. You'll need to find a way to use that list without violating the law. Sometimes this involves you don't contact the alumni directly, but the department does, who will sent you the annonymised results. All this requires quite some investment by the department, so what is in it for them? Maybe they want to add a module to your questionair?