Case: — Caring about whom? About deer (Object with preposition "об"). Они подкармливают оленей зимой.
The word "олени" in the first sentence is the subject, so it must be in the Nominative case.
Case: — Who is living? Deer (Subject). Люди заботятся об оленях.
This guide provides the solution and grammatical analysis for from the 3rd-grade Russian language textbook by T. G. Ramzaeva (specifically the edition from the early 2000s). Exercise Text: "Олени в заповедниках"
Case: — Feeding whom? Deer (Direct object). 2. Grammar Task: Noun Declension