No, the horse is not supposed to stop, hence the "half" halt. It should collect back up underneath you.. it's to rebalance you and the horse. It's supposed to be a slight "pause" of sorts to let you start up again with more collection and control. Think of it like this: you're not getting something right, so you stop for a second and think about how to do it, then keep going... now take out the full stop. (I'm pretty sure that didn't make sense at all...)
Again, I strongly recommend you see a trainer about this, as it is something that really can't be taught without seeing what you're working with.
I'll try and explain it in very very simple terms:
You need the horse to be supple through the body before you even think about getting the head in the right place. You can do this by working on bending through circles, and making sure the horse is moving through the hindquarter. To ask for a headset, you keep the inside rein steady and check and give (like squeezing water out of a sponge) with the outside rein until the horse responds by giving through the jaw and putting its head closer to being in a headset, i.e. lowering the poll. When he flexes, stop bugging him with your hands, and keep them steady. As soon as he raises his head or moves it out of the headset, you want to correct it by asking with the outside rein.
Ideally, I want to see a horse with a long and low headset when first learning, then you can bring the neck up and tucked when you further your dressage training. I like to see the neck flexed and the poll around the height of the wither with the head flexed so the nose is on the vertical..It looks more equitation-horse/ hunt-seat horse but this allows your horse's back to strengthen enough to ask for the "swan neck" in dressage, if you're going that far.
Horse not in headset: http://www.dkimages.com/discover/pre...8/55021333.JPG
Horses nicely flexed in equitation-style/hunt-seat style headset: http://www.loveequestrian.com/Horse_...0FOR%20WEB.JPG http://www.equineformsinc.com/images/02chestmare.gif
Nice Dressage Headset: http://www.horsemagazine.com/2006Sta...otos/Lingh.jpg
Horse Behind the Vertical: http://www.sustainabledressage.com/r...ot/1010731.jpg http://www.pineacresfarm.biz/images/katshow01.gif http://www.sustainabledressage.com/r...lling_back.gif
Horse in front of the Vertical: http://flyingchangefarm.com/alix%20under%20saddle.jpg
Hope this helps.. a bit..?