For in that sleep of death what dreams may come.

[Mithadan]

Bethberry asks,

Can it be that one who died at the hands of the Witch King long ago reaches out to Merry, who will worst the Witch King. Or was the memory imbedded in the Barrow Downs themselves. The Downs were a portal to the past, after all, and in LotR even rocks may have memories.

I think that it is the Barrow-Wight who is to blame for Merry's nightmare rather than the Downs themselves. Our four Hobbit friends were under its spell and were slumbering as they awaited their death. The Wights were not the shades of those buried at the Downs, but rather evil spirits who later came and inhabited the mounds. Laws and Customs of the Eldar makes specific mention of the fact that the unhoused fear of Elves at times become anchored to particular places. So the Wights may be such spirits perhaps sent there by Sauron or the Witch King. Clearly evil, we can assume the Wight delighted in tormenting his victims. The dreams are likely a form of such torment, communicated to his victims by osanwe.