Inline styling for own email templates WooCommerce before version 2.3.x, after version 2.3.x just use the new email template for styles email-styles.php, see Github issue https://github.com/woothemes/woocommerce/issues/5512 and must have gotten some help from a developer per e-mail.

functions.php

function kill_defaults($tags) {
    return array();
}

add_filter( 'woocommerce_email_style_inline_tags', 'kill_defaults', 20 );
add_filter( 'woocommerce_email_style_inline_h1_tag', 'kill_defaults', 20 );
add_filter( 'woocommerce_email_style_inline_h2_tag', 'kill_defaults', 20 );
add_filter( 'woocommerce_email_style_inline_h3_tag', 'kill_defaults', 20 );
add_filter( 'woocommerce_email_style_inline_a_tag', 'kill_defaults', 20 );
add_filter( 'woocommerce_email_style_inline_img_tag', 'kill_defaults', 20 );


function my_email_style_inline_tags($tags) {
  if (!in_array('h2', $tags)) $tags[] = 'h2';
  if (!in_array('h3', $tags)) $tags[] = 'h3';
  if (!in_array('ul', $tags)) $tags[] = 'ul';
  if (!in_array('li', $tags)) $tags[] = 'li';
  return $tags;
}

add_filter('woocommerce_email_style_inline_tags', 'my_email_style_inline_tags', 30);

function my_email_style_inline_h2_tag($styles) {
  $styles['font-size'] = '1em';
  $styles['font-family'] = 'Arial, sans-serif';
  $styles['font-weight'] = 'bold';
  return $styles;
}

function my_email_style_inline_ul_tag($styles) {
  $styles['margin-left'] = '1em';
  $styles['padding-left'] = '0';
  $styles['list-style'] = 'none';
  return $styles;
}

function my_email_style_inline_h3_tag($styles) {
  $styles['font-size'] = '1em';
  $styles['margin-bottom'] = '0';
  $styles['font-weight'] = 'normal';
  $styles['font-family'] = 'Arial, sans-serif';
  return $styles;
}

function my_email_style_inline_li_tag($styles) {
  $styles['margin-left'] = '0';
  return $styles;
}

add_filter('woocommerce_email_style_inline_h2_tag', 'my_email_style_inline_h2_tag', 30);
add_filter('woocommerce_email_style_inline_h3_tag', 'my_email_style_inline_h3_tag', 30);
add_filter('woocommerce_email_style_inline_ul_tag', 'my_email_style_inline_ul_tag', 30);
add_filter('woocommerce_email_style_inline_li_tag', 'my_email_style_inline_li_tag', 30);