The speaker is dead. But the even cooler thing is that we don't know this for sure until the last stanza. So the speaker is a ghost or spirit thinking back to the day of her death. She's actually pretty calm about it too. Maybe because she's been dead for so long she's not so freaked out about it anymore, or maybe she was ready to die when she did; either way, she's completely at ease with it now and looks back at that day almost fondly.
This was a memorable day for her, though. Centuries have passed and she still remembers everything so vividly – what they passed on the way, when she got chilly, what the grave looked like, and she especially remembers the feeling she got when she looked at those horse heads.