When the sentence contains the phrase 'as well as ...,' we do not consider this phrase as part of the subject. So, we only need to check if the main subject is singular or plural. Accordingly, the verb takes the singular or plural form.
Here, the cow is the subject while 'as well as the horse' is not part of the subject. Since cow is singular, the verb will be singular as well. Therefore, the correct answer is option A) Eats. Option B) and option D) are plural verbs (eat and are eating respectively), which would not agree with the singular subject 'cow' whereas option C (eating) is incorrect as it does not fit grammatically in the sentence since it requires a helping verb to make sense in the given context, which is missing in the option.