- For theories about this horn, see: Horn of Winter/Theories.
The old warhorn is a horn made from an auroch’s horn.
It was found buried in a black woolen cloak at the Fist of the First Men by Jon Snow. The black woolen cloak also contained dragonglass. Ghost led Jon to the catch in the woolen cloak. Jon gifted the old warhorn to Samwell Tarly who ended up taking the old warhorn with him to Oldtown.
The warhorn is made from an auroch’s horn and is banded with bronze. On closer examination the horn had proved cracked, and even after Jon cleaned all the dirt out, he was unable to get any sound from it. The rim is chipped as well. It may be ancient. Where it came from and who it belonged to is a mystery.
Some readers suspect that this broken, modest horn may actually be the legendary Horn of Winter, also known as the Horn of Joramun, and they surmise that it may have been broken purposely, or even warded - so that it cannot be blown in error.
During the Great Ranging the Night’s Watch is encamped in the Fist of the First Men. Just after hearing the howling of wolves Jon Snow realizes that something is bothering Ghost and that he wants him to follow him. Concerned about the direwolf’s agitation Jon follows Ghost.
Ghost leads Jon away from the encampment, downhill over a brook and a quarter way round the Fist. Finally at the base of the hill behind a fallen tree he finds Ghost digging furiously at a mound of soft earth.
Jon digs at the loose sandy soil and two feet down his fingers touch cloth and he pulls out a rounded bundle perhaps two feet across. A length of rope binds the bundle together. He slits the rope and turns the bundle and its contents slide out on to the ground, glittering dark and bright. He sees a dozen knives, leaf-shaped spearheads, numerous arrowheads.
Jon picks up a dagger blade, featherlight and shiny black, hiltless. Torchlight moves along its edge, a thin orange line that spoke of razor sharpness. Dragonglass, he thinks to himself. Beneath the dragonglass is an old warhorn, Jon shook the dirt from inside it and a stream of arrowheads fell out. He let them fall and he notices that the wool is good wool, thick, a double weave, damp but not rotted - meaning it could not have been long in the ground. He sees the colour is black and before he stands and shakes it out he realises that it is the black cloak of a Sworn Brother of the Night's Watch. 
A Clash of Kings
Jon Snow finds and gifts the cracked auroch’s warhorn to Samwell Tarly, reasoning that Sam likes old things, even worthless old things. He suggests to Sam that he make a drinking horn out of it to celebrate his part in the Great Ranging beyond the Wall, all the way to the Fist of the First Men. But there is no indication that Sam got round to doing this, or give much thought to the horn. He also gave Sam a spearhead and a dozen arrowheads as well, and passes the rest out among his other friends for luck. 
Later, Sam slays an Other with dragonglass dagger given to him by Jon.
A Feast For Crows
Sam has the horn in the inn where he, Gilly, Maester Aemon, and Dareon stay in Braavos. On the Cinnamon Wind, Sam had to give almost all that they owned in order to pay Quhuru Mo for their passage south from Braavos to Oldtown. By the time the dealing is done Sam is down to boots and blacks and smallclothes - and the broken horn Jon Snow had found on the Fist of the First Men.