An inertial unit doesn't really know your heading; it knows your track, referenced to whatever input keeps it updated, or once updated it before departure.
The air data computer doesn't know heading or track; it knows air pressures.
The magnetic reference system, or compass, knows heading, but not track.
The flight management computer, flight management system, or other computation systems in use collect inputs from various systems on board the airplane, and use these systems to come up with the data that's presented to the pilot.
The ADC provides data which is used for a number of systems on board the airplane, depending on which airplane is in question. Information may be provided to the navigation computers, but also to aircraft instrumentation, pressurization, and engines and engine instrumentation.
Which inputs are used to determine winds aloft really depend on the system in use, but the basic theory is always the same. The computer needs to know how fast it's moving, and in which direction. If the computer knows the heading and track, and the true airspeed, the computer can calculate the wind component...no different than calculating the wind component using a hand-held aluminum E6B computer.
ADC input is but one input to the computer to allow it to make that calculation.