Just like the basalt organs on Szent György hill (see here and here) are not real organs, the ice cave is not a real cave. It's "just" a 10 meters deep cavern formed when pieces from former basalt organs fell down.
Strangely enough cool air is flowing from between the rocks even in the warmth of summer. And even stranger: the locals don't call it the ice cave, but Sárkánybarlang, meaning ... Dragon Cave. According to popular belief Szent György Hill was inhabited by a dragon until murderous "Saint" George came and killed it.