I watched the first 3 episodes of Higurashi No Naku Koro Ni Kai (yes, the second season) and there is no horror, nor is it tagged as "horror" on the site I'm watching it; opposed to the first season.
There are several reasons why this may be the case. Higurashi No Naku Koro Ni Kai is
basically the answer arcs for the "previous season". They do contain and reference the previous season, as they are answers, they would inadvertently reference certain actions/scenes which could be construed as horror. They are, however, notably lighter as they come from the viewpoint of resolution.
As such, depending on your tastes, they might still be considered horrific, or classified as horror. My reference for classification is actually AniDB where they do classify it as horror. It is interesting to note that IMDB also classifies it as horror.