The letters for numbers are only used nowadays in very special contexts. First, note that English also has some usages: when enumerating things in speaking, for example "I did it because, A, I was hungry, B, I don't care what they say, and C, everybody do this". Also I think you'd find "Part A", "Side A / Side B". In all of these, Hebrew may similarly use letters (and I imagine speakers in neither language will go beyond ד/D or so...)
More Hebrew-special uses are rare these days. The two main uses are (A) when specifying the day of the month by the Jewish calendar (ה' באייר); and (B) (See what I did here?) in school grades (= years): כיתה א', כיתה ב', ... כיתה י"ב. Also in book chapters, but there it's equally popular to use modern numbers.
I guess it won't sound strange to also say סטודנט שנה א' באוניברסיטה (along side שנה ראשונה), I'm less sure about continuing it to שנה ד.
Finally, one peculiarity: there is one date of the Gregorian calendar where the Israeli culture uses the Hebrew way for the date of the (Gregorian) month: כ"ט בנובמבר, when it marks https://en.wikipedia.org/wiki/United_Nations_Partition_Plan_for_Palestine#The_vote (the historical occasion or its anniversary).