It looks like your formula returns 0 because COUNTIFS applies AND logic to every condition, so you are asking Excel to count cells where the same position is "H" and "A" at the same time, which can never happen.
If you want to count columns where row 3 is H or A and row 4 is 0, use two COUNTIFS and add them together:
=COUNTIFS(E3:GZ3,"H",E4:GZ4,0)+COUNTIFS(E3:GZ3,"A",E4:GZ4,0)
Or a single formula version:
=SUMPRODUCT((E4:GZ4=0)*((E3:GZ3="H")+(E3:GZ3="A")))
If it still returns 0 then your zeros may be stored as text, in which case replace 0 with "0".
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hth
Marcin