Your hand limit is important for innovations and domesticated animals, since those go into your hand first and get played into your tableau from there.
You will forget this for your first couple of games, get to near the end and realize that you've lost all your elders several times, but still have the Horse card you got from a lucky roll on your first hunt. Generally, you can't keep elders around long enough to build up a hand until you have some mature daughters. So expect that your hand will only be in play in the mid-to-late game. But yeah, only cards you gain during the hunt go into your hand.