Why do some moles grow longer and darker hair than the rest of the skin?
Before answering the question (about the hairs) I will first go in some detail about what moles actually are:


  Moles are growths on the skin that are usually brown or black.  They
  are formed by clusters of melanocytes, the pigmented cells responsible
  for your skin color.  Moles typically appear during the first 30 years
  of life, can be flat or raised, and can darken with sun exposure,
  puberty, or pregnancy.


There are no articles covering this topic in detail (most of them are about the skin cancer, if you are interested in this topic check out this article). However there are some medicial experts talking about the hair growth.


  Joshua Zeichner, M.D., Director of Cosmetic &amp; Clinical Research at the
  Mount Sinai Hospital in New York City. "If the mole also contains a
  hair follicle, the hyper-pigmentation can cause the hair that comes
  out of it to be coarser and darker." 


Junji Takano, a Japanese health researcher said the following about this topic:


  This is due to the fact that capillaries of a mole are growing rapidly
  and excessively, and this includes the hair follicles


Actually moles are benign tumors(wiki), the cells in the body in charge of normal skin color, are being produced at an extremely fast rate. Thus causing the melanocytes to form in clusters instead of spread out, causing abnormal skin pigmentation in some areas of the body(wiki). So based on the above quotes this "fast production" also affects the hairs which are present in this piece of skin. More interesting is that people hate these hairs (which make sense offcourse) but in most of the cases this is a sign that this mole isn't cancerous: 


  A mole that has a hair growing out of it usually means that is was
  present since birth or at a young age and is typically normal.


references: first quote, second quote, third quote, last quote