Slightly different input spec to your code ( and very simplistic output ), but this could easily be modified to suit. Abigail deserves the credit for the leap year code.

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

my $lastday= sub {
     $_[0] == 1 and
         return (
            $_[0] % 4 ?
                28 : $_[0] % 100 ?
                    29 : $_[0] % 400 ? 28 : 29
        );
        return ( qw~ 31 0 31 30 31 30 31 31 30 31 30 31 ~ )[$_[0]];
};

my $mon = $ARGV[0] ? $ARGV[0]-1 : (localtime( time ))[4];

my %days;
@days{ 1 .. $lastday->($mon) } = ();

opendir DIR, './'
        or die "Can\'t read from dir:$!";
for ( grep { /^.*?_weather/ } readdir DIR ) {
        my $day = $1 if /^(\d+?)-/;
        delete $days{$day} if $day;
}
close DIR;

print map {
        join '' => $_, "\n"
} sort { $a <=> $b } keys %days;

__END__
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