Ilya Malyanov, are any of the typical customizations or apps not able to fill this need?
https://apps.shopify.com/uploadery
https://apps.shopify.com/product-customizer
Drag and drop rarely has anything to do with the app side of things and is more about the themes programming which can be handled by open source libraries.
http://www.dropzonejs.com/ (MIT license)
Contact me if you just need an integration or proof of concept for normal methods. paull.newton+myfacepot@gmail.com