Pointy Mountain is where Old Jingle lived in Hooves Of Fire. His house was balanced on the top of the mountain and slide down it if one side of the house had weight on it. After this Jingle decided that he preferred his house at the bottom of the mountain before moments later deciding to push it back onto the top. But this fails and the house slides onto Jingle, trapping him but luckily the Head Elf sees this happen and alerts Robbie about this who is able to get Jingle from under the house by using Sebastian MuscleWhale and OctoMonkey, two toys that he had made in order to lift up the house to pull Jingle out.
It is unknown if Jingle still lives at Pointy Mountain or it he moved into Reindeer Lodge as the location isn't seen again in the two later films Legend of the Lost Tribe and Close Encounters Of The Herd Kind.