How do you add a short description for each product to the checkout page in Woocommerce?

Solution:

The filter woocommerce_get_item_data can be used for that.

Like so:

add_filter( 'woocommerce_get_item_data', 'wc_checkout_description_so_15127954', 10, 2 );

function wc_checkout_description_so_15127954( $other_data, $cart_item )
{
    $post_data = get_post( $cart_item['product_id'] );
    $other_data[] = array( 'name' =>  $post_data->post_excerpt );
    return $other_data;
}

Note that maybe some kind of checking will be needed, e.g., make sure this filter is only called when actually viewing the Checkout page, as I don’t know if it’ll be called in other instances.