With the help below code you can hook order note on cart page. You can submit order note in below custom filed and retrieve it to order notes textarea of check out.I hope it make sense.
add_action(‘woocommerce_cart_collaterals’, ‘my_custom_checkout_field’);
function my_custom_checkout_field() {
echo ‘<div id=”my_custom_checkout_field”><h2>’.__(‘My Field’).'</h2>’;
woocommerce_form_field( ‘my_field_name’, array(
‘type’ => ‘text’,
‘class’ => array(‘my-field-class form-row-wide’),
‘label’ => __(‘Fill in this field’),
‘required’ => true,
‘placeholder’ => __(‘Enter something’),
));
echo ‘</div>’;
}