No, as the mounted creature is still a Medium creature

Being mounted does not change the size of the mounted creature (see the rules on Mounted Combat; PHB, p. 198), so if the Hunter ranger targeted the mounted creature with an attack (taking your example of a human on a horse), the mounted creature (the human) is still Medium and therefore would not qualify for Giant Killer. The horse, being a Large creature, would qualify regardless of whether it was mounted or not.

For reference, the Hunter ranger's Hunter's Prey class feature, the Giant Killer option (PHB, p. 93):

Giant Killer. When a Large or larger creature within 5 feet of you hits or misses with an attack, you can use your reaction to attack that creature immediately after its attack, provided that you can see the creature.

If the mounted creature hits you, it is Medium, so does not provoke this Giant Killer attack, even though it is mounted and the mount is Large. If the mount attacks you, then you will be able to use Giant Killer.