How do engines cope with various intake airflow speeds?
The airplane isn't aware of the winds. It just moves through the air mass at a certain speed, and if the air mass is moving it adds or subtracts from the aircraft's speed over the earth.

Drive your boat along a river with a 10 mph current upstream, then downstream, both at 25 mph on the boat's speedo.  The whole time your boat's showing 25 and the hydrodynamic forces acting on the hull are 25 mph forces. What's your speed relative to the shoreline going upstream compared to going downstream?  15 going upstream and 35 going downstream right?  

Exact same thing with airplanes.  Navigating ships allowing for ocean currents is exactly the same as navigating airplanes in "air currents", they have "tailwind" currents and "headwind" currents and cross currents where you have to aim for point X to actually proceed to point Y, except things are happening in slow motion in the ship.