One interesting thing about this short story is that when it was first published in 1948, in The New Yorker, it generated more mail than any story ever had until that time. I think such a fact explains at least one thing: when it first came out, "The Lottery" was unlike any other story to have ever been told.
As far as "horror" story versus "surprise" story, I think you could make arguments for both, really. While horror is an adjective that could certainly be considered an entire genre in itself, surprise story seems a little less sufficient to stand on its own. If your question suggests that "The Lottery" be fit into one over the other, as a category, I'd say neither of these descriptions fully encompass the entire short story. Yes, the story is horrific, and yes, it is completely shocking. In addition to these descriptions, it has been critiqued as story with such an ambiguous message that its purpose and meaning (and moral, if it has one) are left completely unclear. Was it the author's main purpose to horrify? Was it the author's main purpose to shock? I'm not sure that either of these could be answered with a resounding, "yes."
In this case, I encourage you to judge for yourself, what kind of story this short story is. How were you personally affected? Today's audience has been exposed to so much more on the scale of horrific and shocking, that perhaps it no longer holds the same emotional pull that it did upon its inception. On the other hand, its moral ambiguity, curious characters, and general eerie tone give this story the bulk of its timelessness as, arguably, one of the best short stories written in modern times. Perhaps both horror and surprise here are merely sub-categories to a much more complicated classification system.