Add new Control to Customizer to modify Headings (h1, h2, h3…) Color

as far as I know there is no WordPress Standard Control in the Theme Customizer for a Color Picker. But you can add one with a new Class. Paul underwood made a wonderful tutorial for adding Custom Controls here! And gave examples containing a color picker on github. (NOTE: Please note of the important below comment from WestonRuter, there is now a Color Picker Control in WP).
A simpler approach could be to create a text-field and put your hex-value into it. Threre for you have to create a setting and control in your functions.php. The code in functions.php might looks like the following:

function yourtheme_customize_register($wp_customize) {
//Add new Section for Theme
    $wp_customize->add_section('yourtheme_theme_section', array(
        'title' => __('yourtheme Settings', 'yourtheme'),
       'priority' => 30,
    ));


//  Add new Setting
    $wp_customize->add_setting('headings_color', array(
        'default' => __('Please enter a Quote in Customizer', 'yourtheme'),
    ));

// Add new Control
    $wp_customize->add_control('headings_color_control', array(
        'label' => __('hex color', 'yourtheme'),
        'section' => 'your_theme_section',
        'settings' => 'headings_color',
        'type' => 'text',
    ));
add_action('customize_register', 'yourtheme_customize_register');

You can use the Value from Customizer in your template files (e.g. header.php) with the get_theme_mod() function. e.g.

 <style> h1, h2, h3 {color: <?php echo get_theme_mod('headings_color')  ;?>;}</style>

Hope that will help you.