First let me add a few word of caution here:
Do not use a head halter / halt / holt alone. It can cause serious damage to their neck. Use it in combination with a leash attached to a flat collar or harness. The dog pulls on the leash attached to the collar, and you control the head with another leash. You can also use a cani cross harness for the pulling leash.
I understand it kind of defeat the purpose here, but I think this is a major concern. It is not at all the same problem with horses, the anatomy is quite different (even if it might surely cause problems to horses from time to time).
To answer your question: I don't think you should stop using it because your dog is above one year of age. If your puppy got used to it, there is no reason it would cause additional problems to an older dog. Especially, at 1 year you already have a dog that can pull more than enough to be a problem for the owner or for the dog itself (trachea injuries, or in this case, serious neck injuries). So either it is already harmful or it is not.
However I think that once again it is important to define the real problem here, and to put the solution in a clear and concise way:
Your dogs didn't learn how to walk on leash. The solution is to train them.
You can use as many tools as you want, at the end you have to train the dog. The less tools you use to more you actually teach the dog (vs. control the dog). The first step to train a dog to walk on leash should consists in indoor walks without leash.
So I'm not blaming you here for using it, probably it didn't cause problem to their necks (my first point) and it helped you (your point). So great, now you can go to the next step and train them to walk on leash (I don't want to elaborate too much here, this should be another question and we should add a link).
Let me quote your link:
Using the Halter on Walks
After a few days of short sessions, during which your dog wears her halter and then gets good stuff, you can clip on a lightweight leash and take her for a five-minute walk. Take treats with you, and feed them to your dog when she’s walking beside you, wearing her new halter. If your dog pulls, the leash will tighten and her head will turn to the side. When this happens, encourage your dog to come toward you. When she’s close enough, the leash should go slack again. Make sure it stays completely loose unless your dog pulls and causes it to tighten. (Don’t tighten the leash yourself.) She needs to learn that if she stays close to you, the leash will stay loose and she can walk comfortably.
This is actually a short introducing on how to teach a dog to walk on leash. If you actually train the dog that way then you'll have results, then you can get rid of the halter. It is the same with prong collars: if you train the dog to walk on leash, then you can remove the prong collar. Additionally I think it is also of importance regarding my first point (neck injuries): if you use the halter to train the dog during "five-minute walks", then why not. You're likely to pay attention to the dog and limit the risk. If then you take the dog with the halter for "regular" walks, even with a proper leash training there is the risk that the dog would lunge at a car/other dog/baby and risk to injure himself.
These 2 pages elaborate on the pro's and con's of the use of halt: