Is it possible to retrieve easily all the Nature papers featured the cover since 1950?
If you are researching a specific area (doing a lit search) then your university library and an academic librarian is a good place to start. Libraries normally have access to such things and can get copies of papers. The librarians know how to go about it and can even help you manage a broader search. 

All you really need is some specific idea of what you are after. A citation in a recent paper is an excellent start. Even if your own university doesn't have direct access, they likely have associations that they can work through to obtain what you want. 

There was a time, pre internet, when this was the primary way of doing academic research. 

I hope I've interpreted your need correctly.