Yawning is often thought of as a stress release but there are so many other reasons not associated with stress at all. It is not just the yawn but the movement of the tongue during and after the yawn that may indicate an attempt to clear out debris or distribute saliva.
The first thought is that there is something stuck between the teeth and cheeks. This is very common especially when there is limited tongue movement due to pain from sharp dental points. However, this cause may not apply to your horse because you haven’t fed her yet – but I needed to put this first because it is the most common reason for an exaggerated jaw movement – what people often confuse as “yawning.” A lot of horses yawn as soon as I remove the sharp points of the last few cheek teeth – BIG yawns as they check out their new smooth edges.
An associated reason also based in dental pain is that many horses place food between the cheeks and teeth to protect the cheeks from the sharp teeth. Opening the mouth wide allows her to get in and clear out the old food before adding new food. This is also common in horses with sharp teeth. Whether this packing of food is on purpose or is just secondary to an unwillingness to make the final clean up is unknown. Some horses make a formed ball of food soaked in saliva that keeps the area lubricated and protected. I pull these balls out before floating – the size of a golf ball.
In some horses there is a space between the last upper cheek tooth and the gums where food becomes trapped and can’t get out until the next meal. This food has turnover as it never has the fermenting smell of long trapped food. Most horses do not have this space or problem.
If the last few upper and lower cheek teeth have sharp points then get those filed smooth to determine if sharp points are at the root of your horse yawning. Remember, not all dentists remove all of these edges so find a dentist who can.
Another reason is that there is decreased production of saliva and opening the jaw wide helps in the distribution of newly formed saliva created by the anticipation of receiving food. Usually the ducts empty along the midpoint of the cheek teeth but maybe there is a different location not allowing for even distribution. Or there is a decreased amount being produced requiring your horse to distribute it by jaw and tongue movements.
The important point taken from your description is that you horse has no problems chewing or swallowing. I just don’t believe it can be stress as you make no other mention of stress behavior such as pacing, pawing, kicking, aggression, etc.
As always, be leery of free choice hay (as you say) because feeding more hay than needed only adds starch in excess of her needs. This is the ONLY way to develop insulin resistance which seems to be at the root of all other problems in the horse (inflammation, laminitis, obesity, chronic protein deficiency). The rough average is 1.5% of body weight in forage or 15 pounds total forage (hay + pasture) per 1000 pounds – 7.5kg forage per 500kg body weight.