Look into the File::Glob module to get your file list (perldoc File::Glob).
You can use regular expressions to look for filename matches (perldoc perlre), it'll look something like:
if ($filename ~= m/DATE_/)
For the date comparison, are you going to use a system date, or is there some sort of naming convention that integrates the date into the file name? If the latter, regular expressions are your friend again.