You can have eyes open or closed, anytime during all 4.
Try not to lock on to any one thing in your field of vision. Master Lama Rasaji sometimes describes it at paint brushing the room with your eyes. (Energy flows out the eyes as well. We want that to continue and increase)
The reason I mention the horizon is that a lot of people unconsciously look down to do the exercises and their head then tips toward the earth, changing the alignment of their spine.
If your spine is elongated throughout, and your posture remains good, dont concern yourself too much with the horizon.
Guiding people to find the horizon is the easiest, fastest and most reliable way to correct their physical posture related to the head and neck from a distance.