my @log_files = ...[ read list of files from dir ]...;

if (@log_files) {
   my $newest_idx   = 0;
   my $newest_mtime = -M $log_files[0];
   for my $idx (1..$#log_files) {
      my $mtime = -M $log_files[$idx];
      next if $mtime < $newest_mtime;
      $newest_idx   = $idx;
      $newest_mtime = $mtime;
   }

   # Leave newest alone.
   splice(@log_files, $newest_idx, 1, ());
}

for my $log_file (@log_files) {
   ...[ process $log_file ]...
}