Try altering the following code to show your problem if it doesn't do what you are trying to achieve already:

use strict;
use warnings;
use Data::Dumper;

my @prizes =
  (
    {
    'Timestamp' => '2005-11-07 11:18:01',
    'WinnerId' => '2026',
    'lineid' => '2026',
    },
    {
    'Timestamp' => '2005-01-07 11:18:01',
    'WinnerId' => '2001',
    'lineid' => '2001',
    },
    {
    'Timestamp' => '2005-05-07 11:18:01',
    'WinnerId' => '2015',
    'lineid' => '2015',
    },
  );
    
my %month =
  (
  '01' => 'January',
  '02' => 'February',
  '03' => 'March',
  '04' => 'April',
  '05' => 'May',
  '06' => 'June',
  '07' => 'July',
  '08' => 'August',
  '09' => 'September',
  '10' => 'October',
  '11' => 'November',
  '12' => 'December',
  );

my @mapped_prizes = map {[$month{(split (/-/, $_->{'Timestamp'}))[1]} 
+=> $_]} @prizes;

print Dumper (\@mapped_prizes);
[download]

Prints:

$VAR1 = [
          [
            'November',
            {
              'Timestamp' => '2005-11-07 11:18:01',
              'lineid' => '2026',
              'WinnerId' => '2026'
            }
          ],
          [
            'January',
            {
              'Timestamp' => '2005-01-07 11:18:01',
              'lineid' => '2001',
              'WinnerId' => '2001'
            }
          ],
          [
            'May',
            {
              'Timestamp' => '2005-05-07 11:18:01',
              'lineid' => '2015',
              'WinnerId' => '2015'
            }
          ]
        ];
[download]

Note that I removed some of the fields from the hash - only a couple are needed to demonstrate the issue. Note also that I added a couple of entries because it seems that more than one is required to show the issue. And further, note that I reduced the reference nesting by a level in the @prizes array which cleans up the warnings that I was seeing and also that I changed the +{}, in your original map (that looks rather peculiar) to a more usual {} and altered the contents of the map expression to do what I guess you want to do: generate an list of pairs of month and prize elements. I don't see why you don't want this as a hash however.