Paris Jackson -- Spends the Day with Mom ... on Grandma's Birthday

Paris Jackson spent most of Saturday with her biological mother Debbie Rowe -- looking at horses, playing with her hair ... real mother/daughter stuff -- and what's particularly interesting ... they were hanging the same day as grandma Katherine Jackson's birthday.

Paris and Debbie were way out in Palmdale, CA where Debbie lives -- so if Paris saw Katherine at all yesterday ... it wasn't for long.