The horses tongue attaches to the Hyoid bone (see photos) The hyoid is Intimately connected to the airways and therefore affects the horses breathing, and is connected to hind limb via fascial. See right:

Sternohyoideus connects the hyoid to the sternum Omohyoideus connects the hyoid to the inside of the shoulder -Direct connection from the tongue to the sternum and shoulder along the bottom of the horse’s neck.
Tension in the tongue – tension in sternum horse can’t lift through back to allow for collection- affects hindquarters Small muscles also connect the hyoid bones to the temporomandibular joint (TMJ) and the poll. The TMJ is an important center for nerves that control the horse’s balance and proprioception. And the poll-its ability to bend and flex-is of central concern to the dressage rider. Because
of the small muscles connecting them, there is a very close relationship (which few riders know about) between the horse’s tongue, hyoid bones, TMJ, poll, head, and neck. “When the horse’s tongue is free and soft, all of this translates into a horse who is better able to move well, with coordination, improved balance, and a significantly lengthened stride. Therefore using the correct bit to allow tongue freedom has much more importance than you would first think.

(L.Tellington- Jones 2013)

L.Tellington-Jones (2013) Dressage with Mind, Body & Soul: A 21st-century Approach to the Science and Spirituality of Riding and Horse-and-rider Well-being.Trafalga Square