Yes, most of the time, you get to play the first enhancement when using a character with swift horses on it, but there are a few exceptions. Ethiopian Treasurer will get to play the first enhancement before you are able to block, but you can still play the next enhancement with swift horses seeing as it is a play next, not play first card. When you encounter a situation where the hero has the ability to play the first enhancement once the blocker is presented, you will still usually be able to play the first enhancement, as swift horses interrupts those abilities, unless of course the hero's ability to play the first enhancement after blocker is presented ability is cannot be interrupted as in the case of Michael and angel's sword.
