But now I'm stumped.......today he spent most of the walking time on a loose rein, and he kept his head real low and neck and back stretched for the whole time....I realized he was 'stretching' but I wanted him to pick his head up a bit more (right? Silly I know, when most people want the head down!) I did pick him up with the reins, used my legs to push him forward, but as soon as he backed off the bit his head would go straight back down......what's this horse doing? Is he too lazy to carry his own head? Is he sore? (he worked fine) is he avoiding something? Is he responding to all the collection by rounding like that even at a relaxed walk?
Stretching the neck out, and the head down, stretches the muscles over the back and along the top of the neck. It's a good thing, and you should use that during your warmup, cool down, and periodically while working, in order to allow the horse to stretch out those muscles that you're asking him to use.
If, while you're working, you don't want the head so low, then you'll have to move the hind end up under the horse more (don't think of it as lifting the head).
My current horse has a naturally high head carriage (think giraffe). But whenever she's on a free rein she stretches her head and neck down and out.
The only time the stretching/lowering of the head is an issue is if the horse is leaning on the reins for support. At that point, it's an issue with the hind end, not the head (not enough engagement/balance). I bump the hind end up first, then half-halt, to remind the horse to carry itself (not lean on me for support).
What is "a correction bit"?