If you use a tie-down or martingale on your trail horse, be sure to unfasten it from your bridle before every water crossing. If the water is deep, your horse could drown if he were suddenly unable to raise his head above the water. And even if the crossing looks shallow and safe, your horse could slip, slide, or step into a hole, forcing his head underwater.
Better yet, train your horse so that he learns to relax, soften his poll, and hold his head at a natural level, so that you won't be tempted to use a tie-down in the first place. You'll have more control, and your horse will be better able to balance himself on the trail, especially when going up and down hills. And you won't face the risks associated with tying your horse's head into one position on the trail.