The job of the freelancer it is not easy. In particular in Italy. Moreover, if one does not have Italian or UE citizenship, to the “normal” difficulties another important one has to be added:
To obtain an entry Visa to enter and live in Italy. Generally speaking, the most suitable one for freelancers is the “Autonomous Work” Visa but the freelancer not always is able to get all the documents requested for that kind of Visa. For some freelancers, the most indicated Visa is for “Residenza Elettiva” (Elective Residency). If the activity of freelancer is only a temporary job, for example waiting for completing a course, the Visa to request is for “Study”.
The kind of activities that fall into the category of “freelancer” are too many to list and every day they grows further in number. It is sufficient to surf the net and go to web pages like in order to understand.
Some of the jobs included in that webpage, even if they are autonomous work activities, contemplates in Italy the possession of special licenses or professional titles etc… that is not easy at all for No-EU citizens. To go deeper into the matter please let have a look on my article: L’eccessivo numero di attività professionali regolamentate limita la competitività italiana 
For some kind of freelancers, like translators, the Law provides Visa ad hoc like the one for Translators and Interpreters (ex art. 27 lett. D)
Thanks to our experience, Studio Papperini Relocation,  can say that in many occasions, the difficulties to obtain the Visa have a “lexical” nature. Very often is important how the activity is presented, with the right words, because with the right lexical term one can be able to enter in a kind of Visa entry. 
Don’t hesitate to contact us and we will try to help you to plan the most suitable Visa request according to the specific activity you intend to do in Italy.

Giovanni Papperini