Just wondering.

Yes.

Sacrifying is the cost, removing is the effect.

You can pay a cost even if you can't apply an effect .

The keyword here is "to", as described in the rulebook.

Do this TO do that.

Yep. It doesn't target a damaged Hoth objective, so one is not required. Killing Cold is pretty much a must-run in an Executor deck for that ability.

So, I assume it is the same with "Feeding the Pit"? Can I sacrifice the unit to remove 0 damage? Do I still draw the card?

So, I assume it is the same with "Feeding the Pit"? Can I sacrifice the unit to remove 0 damage? Do I still draw the card?

You can sacrifice the captured card to remove 0 damage, but you would not get to draw a card in that case. Still could be a good idea if the LS is about to destroy the objective and you don't want them to get the unit back in hand.

Cool, thank you.

Since it wasn't mentioned, the reason you can't draw a card in that case is because drawing a card is part of a "then" clause, and to resolve a then clause, you have to completely resolve the effect before it. In this case, you have to remove one damage.