Add input fields in the cart page and save the data in a dateset

You can implement such functionality, however, in order to do that you’ll need to create your Store using custom code and pages (not Wix Stores pages). This way you will be able to get all of the data needed and fully interact with it using Wix Stores API.

You can find more information about it here:
https://support.wix.com/en/corvid-by-wix/wix-stores-with-corvid
https://www.wix.com/corvid/reference/wix-stores.html

Please note, that you can simply add a Buyer Note link to your cart page as it is described here: https://support.wix.com/en/article/creating-and-viewing-buyer-notes-in-wix-stores