use POSIX 'strftime';
my $date = strftime '%Y%m%d', localtime;

my $re = qr/whatever/;
my $count = 0;

for (glob "/path/to/*$date*") {
    local $/;  # to slurp
    open my $fh, '<', $_ or warn $! and next;
    my $content = <$fh>;
    close $fh;
    $count += () = $content =~ /$re/g;
}

print $count,$/;