Hori refers to carved ceramics. This may be simply an incised decoration in the body of the piece of pottery or may include carving a design through and outer layer of glaze to expose an inner glaze of a different color prior to firing of the pot.

A iron glazed Hori style “Ju” chawan by LNT Shimizu Uichi with the kanji for “Longevity” inscribed on the pot.
Hori style mizusashi by LNT Shimizu Uichi. Kangi inscribed on the mizusashi are for “Setsugekka” or “Snow, Moon, Flowers”.