First I'd like to say that this question is not a very nice one. Regardless, let's go through this.

A. One of the biggest problems with this choice is that if we are using an "ing" verb, these will be actions performed by the farmer as a result of keeping them cool or in order to keep them cool. While grammatically this works, I don't see how "providing [cows] with high-energy feed" and "milking [cows] regularly" would keep them cool. Also, the "are producing" portion is awkward; "produce" would be correct.
B. "The Holstein cow" is incorrect; needs to be plural to refer back to "them".
C. Parallelism - "provided" vs "milking"; keep verbs in the same tense/form.
D. "The Holstein cow" is incorrect; needs to be plural to refer back to "them".
E. Correct. For the farmer who takes care to keep [the cows] (a) cool, (b) provided with high-energy feed, and (c) milked regularly, Holstein cows will [subsequently] produce an average of 2,275 gallons of milk each year.

[spoiler]Answer: E[/spoiler]

Thank you both. I guess I was in such a rush when I initially answered the question and reviewed incorrect answers from that practice round that I somehow overlooked the plural pronoun in the early part of the sentence

...great reminder to be more careful moving forward