You could use the field calculator and something like:
def FieldCount(fld1,fld2, ...):
fields = [fld1, fld2, ...]
return sum(f > 0 for f in fields)
FieldCount( !F01!, !F02!, ... )
Or this for the function:
def FieldCount(fld1,fld2, ...):
return sum(v > 0 for k, v in locals().iteritems())
Also look at Joshua Bixby's answer in this thread.