Yes, but that’s assuming that the horse is strong enough to put his head down that low without falling on the forehand. In fact, the horses’s strength is part of what being demonstrated in this movement.
OP, I would suggest a few things.
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Don’t sacrifice the horse’s balance for a head position. When he is stronger, he will be able to put his head wherever without losing his balance. Stick to your guns and to the task of being fair to your horse.
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When you halfhalt, make sure that your last part of that aid is a soft release of the reins (perhaps invisible to the onlooker) that lets your horse know that after he has brought his balance back, he can/should open back up his poll and telescope out from the base of his neck as much as he can or would wish to.
IMO, there’s too much emphasis on “the contact” (which people start to mean "pushing into the bridle), and that can turn into too much holding with the hand, in pursuit of that feel. To me, that’s digging a training hole that’s hard to fix. It’s also kind of a bummer for the horse.
- Assuming you have taught your horse to seek out contact with the bit with whatever length of rein you offer, there are a couple of equitation recommendations I’d offer to you as you ride the stretchy trot.
– check yourself to make sure you haven’t leaned forward, or collapsed the front of your body. Having short arms myself, I wouldn’t mind if you had to lean just a touch forward to help give him that space in front (if/when he gets to that place where he can reach down far and you are almost on the buckle.) But! continue to support yourself in your core. Make yourself still and easy to carry,
– Post slower. This helps a horse continue to find his hind leg and push from back there as opposed to rushing a bit. Rushing, taking shorter steps, is a horse who is essentially falling on the forehand and stepping out quickly with each front leg to catch himself.
I like to do these two things to modify my own eq first, to make my own balance “back,” slow and strong a couple of strides before slipping my horse the reins. This way, I have told him with my body where the balance should be and now I’m allowing him to modify his own head and neck position as he can/would like to gain some freedom there.
To me, this is part of making the horse’s overall balance independent of the reins. That’s a nicer deal for the horse and, IMO, it’s generally a more correct way to ride a horse (though plenty of dressage theory would make it appear otherwise).
I hope this helps!