Pogonophilia may not only involve an attraction to beards, but a desire to touch and run one's fingers through them.
More About Pogonophilia
This term comes from the Greek word for beard "pogon." The popularity of beards and mustaches has fluctuated based on men's fashion. In more recent years, mustaches and beards have been popularized by Movember, a month-long charity event held through November to raise funds and bring awareness to men's health issues, particularly prostate cancer. In the past, beards have been seen as a sign of maturity, power, and respect.