One thing you need to do periodically as a hornist is hang your mute from your wrist to make a quick switch from open to closed or closed to open.
Closed to open it probably does not matter much how long the string is. Open to closed however my suggestion is that the string needs to be just long enough to reach the mute comfortably as you turn your hand around. This is so you can make the fast switch with just a quick flick of your wrist and grab the mute so that you can insert it.
If the string is too long, as in the second photo, you can’t easily reach the mute to grab it.
In any case, this is one of those topics that is one that will eventually come up for the advancing horn player. Check out your mute and see where it stands in terms of that string.