The Snowy Owl can be found all over Winterspring -- there are no specific spawn locations. Pet quality starts at Poor and goes all the way up to the coveted Rare. While we do know that December 21 was the first day of winter in Warcraft, we don't quite know as of yet when these owls will stop spawning -- last year it was the end of February. However, if the spawns are matching up to real life spring, the owls should disappear at the Spring Equinox, which is March 20, 2014. Because this isn't really guaranteed or known information at the present time, it's highly recommended to simply go catch your owl now, while we know they're available.
The Snowy Owl is required for the Kalimdor Safari achievement, which in turn is required for the World Safari achievement. Completing World Safari will net you the Zookeeper title, so players that would like the title should definitely go pick up the pet. And even if you don't care about the title, I'd pick up an owl anyway. With fast attack speeds and deadly abilities like Predatory Strike, they're a nice addition to any Battle Pet team.