Cribbing collars are causing unpleasant pressure on the horse's throat when cribbing and in that way preventing the horse from doing so. It is possible for cribbing collars to constrict the trachea, but only when they are used incorrectly. It is important to make sure these cribbing collars are fitted properly and do not cause pain, otherwise they will only exacerbate the behaviour.
However, cribbing collars are not recommended unless cribbing is creating serious problems for the horse. It would be best to try changing the horses' diet or environment before cribbing collars are used. It is also important to remember that cribbing is natural and may not need to be fully curtailed.