#!/usr/bin/perl -w
use strict;

my $dir = 'path to directory';
opendir (DIR, "$dir") || die "Cannot open directory: $!\n";

print "Starting Delete Process\n\n";

while ($_ = readdir(DIR)) {
    print $_, "\n";
    unless (/^\./) {
        if (/\.log$/i or /\.\d+\w+\-\d+\wm$/i or /\.txt$/i) {
            unlink("$dir/$_") if (-f "$dir/$_") ||
                warn "Cannot delete $_: $!\n";
        }
    }
}
print "\nDeleted all requested files.\n";
closedir(DIR);
[download]

As Dermot says, im not sure about that time/date expression of yours, so please post the date format.
I tested this code and it works just fine on my linux box, i guess you have to change the shebang. Both in my and your code.
This will delete all files with extention log, txt or date/time.
Update: added unless{} to not touch files that start with "." (didn't know they where allowed in windows ;)