How to add a new column with text fields to WooCommerce Cart List?

This requires you to override WooCommerce templates:

1) First read: Template structure & Overriding templates via a theme to understand how you can change some templates copying them to your active theme folder

2) Copy the template templates/cart/cart.php located in your Woocommerce plugin to your active theme in woocommerce/cart/cart.php (so not in a “template” subfoder).

3) Open edit the template cart.php and make the necessary changes in the html structure, adding your custom column and related php code.