As for the single-pass problem, you can do that too:

use List::Util qw(reduce);

@hash{$set}{qw(min max)} = @{ reduce {
    return [ $a, $b ] if 'ARRAY' ne ref $a;
    return
        $a->[0] < $b ? [ $b, $a->[1] ] :
        $a->[1] > $b ? [ $a->[0], $b ] :
        $a;
} @{$hash{$set}{data}} };
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Admittedly more hoop jumping here. Of course that doesn't address the memory problem, but in that case I'd still opt for a counter in a while loop instead. (In keeping with the corresponding use of while and each to traverse a hash.)

for my $min ($hash{$set}{min}) {
    my $data = $hash{$set}{data};
    my $i = -1;
    while(++$i < @$data) {
        $min = $min < $data->{$i}
            ? $min
            : $data->{$i};
    }
}
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Makeshifts last the longest.