If you're asking about getting in: as long as you have all of the prereq's and do well in them, it doesn't really matter what your undergrad major is. If you struggled in the pre-req's, then it might help your application to either retake the ones you did poorly in or take some more upper level science classes to prove that you can deal with the workload -- schools seem to vary in which they prefer.
If you're asking about applying food science as a graduate vet, you could work in food animal/slaughterhouse inspection, as a food-animal vet advising farmers on herd health and sustainability, or work for government agencies such as the USDA or the FDA, where you could be involved in inspection (e.g., APHIS), outreach and education, formulating or at least informing policy, and/or research.
I'm sure someone else will come along and give you some more cogent advice. I know more about equine related topics, but I sure do appreciate the vets who work in the food production/animal agriculture field. 🙂