Actually, I thought a horse was an excellent choice. Finding gas will become increasingly difficult. Care and feeding of a horse may be more demanding than a car, but far more sustainable in a post-apocalyptic environment. A horse also works well as a second pair of eyes. Not necessarily, literal eyes, their hearing and sense of smell are better than a human's and could alert you to danger before you see it.
Also, if he encountered trouble, as he did, it would be (in theory) easier to outrun on horseback than foot. The angles they used did not satisfy my curiosity on how he got so easily surrounded. At first sign of a large group of zombies, I would have turned tail and run...er...galloped off. But then, as mentioned above, if the characters always did the smart thing, there would not be much of a show.
I was sad to see the horse get chomped. Even then, its sacrificed allowed the deputy-sherrif to escape. At worst, I think he should have tried to put something over the horseshoes to muffle the noise. Beyond that, I think the horse was a much better option than a car or going in on foot.