The cave (if cave it be) is right above the ship's flag and right next to the trees. You'll see trees, and then wavy lines that "seem" to imply a cliffside, and then a little black arch. Looks like the letter "D" turned on it's side. That's the cave.
Or maybe not. But that's really all the spur/arrow could be pointing to.
And yes, that is a snake on Death's saddle. Which, like the cave, relates to the underworld. As does the myth of Kore/Persephone, which the Death card can very much relate to. The world goes into winter, and Kore goes underground into the underworld. When spring comes--as it will (Death leading to rebirth, Winter to spring), then Kore will return from the underworld. She will emerge from the cave.
This was all part of the great, Eleusinian mysteries--that change over from life to death and back to life represented by Demeter's daughter going underground and then returning. Very apt.
And I agree that the ship and the river bring to mind the River Styx, again reinforcing the Kore/Greek Underworld connection.