Airflow is horizontal only in level flight ! not in climb or descent
If by horizontal you mean at AoA ~ 0 degrees, that is very, very incorrect
The quoted "airflow is horizontal", was in ref to the AoA vane, whatever it reads, is measuring the airflow, and is the basis for the AoA of the wings.
In my context, "horizontal" is relative. Much the same as indicated airspeed and the jetsteam and of course, groundspeed.
It is of course, mounted to the fuselage, so there is already the inherent offset to the angle of attack of the wings vs the fuselage.