I've done some interesting things abroad - formal study abroad programs and some research. While they're great experiences, your grades are still the number one feature that will get you into vet school. If you have good grades, then, yes, something like a study abroad could make a difference between you and another applicant.
It's not really clear cut though. As others have mentioned, it might give you a leg up on some other applicants but as for being the thing that will get you in, probably not.
Plus, it's not pleasant to think about, sometimes bad things can happen when you travel abroad, especially in countries that don't have great roads and medical infrastructure. I had to deal with a major injury abroad a few years ago and the whole incident threw me off track with my graduate degree and applying to vet school. At least now it makes an interesting story for essays and interviews.
Just be sure it's something you really want to do.