The traversal is easy as already shown. The next step is to build a list of counts. Consider:

use strict;
use warnings;
use Data::Dump::Streamer;

my @AoA = (
           [ "X", "Z", "W", "X", "Z", "Z" ],
           [ "Z", "Z", "X", "X", "X", "W" ],
           [ "X", "Z", "X", "W", "W", "W" ],
           [ "Z", "X", "W", "X", "Z", "Z" ],
           [ "Z", "X", "W", "X", "X", "W" ],
           [ "Z", "X", "X", "X", "Z", "W" ],
    );

my @sums;

for my $row (0 .. $#AoA) {
    for my $col (0 .. $#{$AoA[$row]}) {
        ++${$sums[$col]}{$AoA[$row][$col]};
        ++${$sums[$col]}{total};
    }
}

Dump \@sums;
[download]

Prints:

$ARRAY1 = [
            {
              total => 6,
              X     => 2,
              Z     => 4
            },
            {
              total => 6,
              X     => 3,
              Z     => 3
            },
            {
              total => 6,
              W     => 3,
              X     => 3
            },
            {
              total => 6,
              W     => 1,
              X     => 5
            },
            {
              total => 6,
              W     => 1,
              X     => 2,
              Z     => 3
            },
            {
              total => 6,
              W     => 4,
              Z     => 2
            }
          ];
[download]

'total' isn't required if there are no missing rows, but may be a good sanity check. The remainder of the solution is left as an exercise for the reader.

BTW: you can't have a tie with the threshold at 60%, it must be 50% or less. Indeed your sumple supports 50% or there wouldn't be a Z for the penultimate column.