There have been a few oil mines. Oil is mostly at depths below 2000 ft, although there are a number of shallower prospects. The oil at shallow depths is generally low gravity (extra thick) and not as valuable.Tar sands are oil sands where all the light components have evaporated or were never formed.
  A horizontal hole is in essence a type of oil mine. After the main pressure in the formation is depleted, a lot of oil will still seep into the borehole from gravity and can be pumped out. The horizontal wells can be drilled up to a mile in length through oil productive rocks which increases the well's exposure to the formation by a huge amount.
  So the answer is that oil mining is already being done. Good idea, though.