Dominion - Can you trash horses?
Yes, you can.
There is nothing about being part of the supply that affects trashing; they are still &quot;cards&quot; and thus are affected by things that talk about cards.
The rules for trashing from the base game rulebook don't say anything that would restrict it to supply cards:

&quot;Trash a card&quot; - Put a card into the Trash pile.

This is a way of getting rid of a card; a trashed card is no longer one of your cards.


&quot;Gaining&quot; is different because of the rules for gaining itself; the rules for &quot;gain a card&quot; include that the card must be from the supply unless specifically said otherwise.

&quot;Gain a card&quot; - Take a card from the Supply and put it into your discard pile.

Sometimes a card will let you gain a card from a place other than the Supply, but by default
gained cards come from the Supply.


Now, your specific example of Improve and Horses is tricky because normally you wouldn't have a Horse in play at the start of cleanup; since it returns itself to its pile when you play it. But with things like Ways from Menagerie, there are ways to do it.