Damage is dealt as a single lump. There can be multiple triggers that occur off of that lump that happen in some sequential order (akin to how you sequentially resolve X different HI triggers when apocalypse is played), but the damage itself is all at once, and the cards are trashed all at once.
IHW actually proves this; if I take 3 damage with an IHW in hand and two other cards, the IHW draws will not be considered candidates for taking the damage, even if IHW was the first damage "chosen" (because IHW doesn't actually draw the cards until all damage is chosen, and subsequently dealt).
Tethering this back to Skorpios, they would get to see all three damage from the Snare! Before making their choice.
However, and perhaps obviously, but separate sources of damage are resolved independently. For example, if the runner hits a Snare! with Mr. Stone in play, Skorpios must choose if he wants to fire on the Snare! Damage before seeing the Mr. Stone damage. By the same token, if Skorpios had a HI installed and the runner played Apocalypse, Skorpios would have to make their choice after each individual damage (as it is X 1 damage triggers, not 1 X damage trigger).
Hope that helps.