As @Marina replied in his excellent technical presentation (for beef cattle)^, it depends on what your acreage will grow. If you raise a cow on a feedlot and fatten him with corn, then it takes very little “space”. But if all you have is poor, dry range grass, then it’s going to take a lot more of that acreage.
I’m sure that “winter” is going to play a part in this too, but I don’t know what part.
I don’t know a damn thing about raising beef or milk cattle, and what the differences might be. But if you define your inputs (tell us what kind of acreage you’ve got) and your expected outputs (milk, or meat?), then perhaps you can get a very close approximation.
^ Followed by @snarp, but I hadn’t seen that response.