Need to have an archive widget which organizes and displays a custom post type using a custom date field

Yep. You can add a meta_query parameter to methods that query posts, such as WP_Query. This one below gets a custom post type between two dates (which are custom fields created by ‘advanced custom fields’ plugin) and sorts on one of these dates:

$args = array(
    'post_type' => 'event',
    'posts_per_page' => '-1',
    'post_status' => array( 'private','publish' ),

    'meta_key' =>'start_date',
    'orderby' => 'meta_value_num',
    'order' => 'asc',

    'meta_query' => array(
        'relation' => 'OR',
        array(
            'key' => 'end_date',
            'value' => array(strtotime('20130101'),strtotime('20140101')),
            'compare' => 'BETWEEN',
            'type' => 'NUMERIC'
        ),
        array(
            'key' => 'start_date',
            'value' => array(strtotime('20130101'),strtotime('20140101')),
            'compare' => 'BETWEEN',
            'type' => 'NUMERIC'
        )
    )
);
$search = new WP_Query($args);

if ( $search->have_posts() ):

    setlocale(LC_ALL, 'nl_NL.UTF-8');

    while ( $search->have_posts() ) : $search->the_post();

        $start_date = get_post_meta(get_the_ID(), 'start_date', true);
        $end_date = get_post_meta(get_the_ID(), 'end_date', true);
        $start = strftime( '%A %e %B %Y', strtotime( $start_date ) );
        $end = strftime( '%A %e %B %Y', strtotime( $end_date ) );


        echo "$start ($start_date) - $end ($end_date) <br />";

    endwhile;
endif;

See here also: http://codex.wordpress.org/Class_Reference/WP_Query#Custom_Field_Parameters

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