A bridle path is...two completely different things. It can refer to:
1. A trail set aside primary for equestrian use.
2. A strip shaved or cut from the mane behind the ears in order to make it easier to get the bridle on and off.
(Usually, fortunately, context makes it clear).
This Arabian has an excessively long bridle path, common for the breed. (Image source: Montanabw via Wikimedia Commons). In general, English riders cut a shorter bridle path (just enough for the leather) and western people prefer a longer one.