Hi, I don't think what you decide to major in will influence what the admissions committee will ultimately decide on. You can complete your pre-reqs in any degree. An animal science degree may offer an advantage by giving you more "hands-on" experience with domestic and companion animals. On the other hand, a biology degree can give you an advantage with the more theoretical courses in vet school (e.g. anatomy...). I'm just speaking on the terms of the post-secondary institutes where I'm from. Both UCVM and WCVM have accepted students with only 2 years of pre-professional study, and they're getting along fine (from what I've heard!).
My background? I'm a typical city girl who never touched a cow prior to vet school, classically trained at the music conservatory in piano performance, then decided to go to university in the sciences stream, completed an honours degree in zoology in 4 years...my electives included: systematics and evolution, freshwater ecology, entomology (5 courses!), population ecology, vertebrate diversity...the point is to show you that I didn't really worry too much about focusing too much on taking "vet-oriented" courses. I took what I thought was interesting, not to make my application look good. It made my undergrad experience enjoyable.
That being said, I've heard wonderful stories from my classmates who did the animal sciences route. Even if you took the biology route, you can still take animal science courses as electives and vice versa. In my school there are people who have degrees in music, business, forestry, chemistry, ecology, biochemistry, so anything really!
Whatever you decide to choose, make sure you speak to an adviser to make sure you complete your pre-reqs AND to also make sure you complete your degree requirements. Go with your gut and in the end, you're striving for the same dream! I hope this helps and good luck!