Hi,
With the Business edition, you can easily do that by creating a custom field of the table "order" and of the type "text area" via the menu Display>Custom fields.
There is no option to do that with the Essential or Starter edition, but if you're a developer, you can always add custom HTML for your input field in the checkout views, and develop a custom HikaShop plugin to save the data in the order.
If you need to upgrade form the Essential to the Business edition, you can do it here:
www.hikashop.com/extensions/upgrade-my-version.html