Why is the autopilot of the DHC-6 Twin Otter powered by bleed air?
The reason (back in the day) was an envisioned low-cost autopilot ownership in smaller planes,$^1$ but it was a troublesome system as it aged.


  The first production [Twin Otter] aircraft left the Downsview factory with an option for the Honeywell H-14 autopilot. This system used large pneumatic servos to control the aircraft. This was a popular option at the time however as the aircraft and autopilot aged the maintenance involved in keeping the system serviceable resulted in many operators disabling or removing the system (rockymountainaircraft.ca).


It works via pneumatic servos; pistons that are actuated by pressurized air.


  
  Source: NASA




$^1$: NASA contractor report (prepared by Honeywell) on "fluidic" flight control systems (also covers the aforementioned Honeywell H-14 autopilot).