Cold Emailing as a Freshmen from a Non-Target

Hi! I'm currently a freshmen attending essentially a nontarget in NYC and was looking for advice in terms of cold-emailing. Is it currently an appropriate time to start looking for internships for next summer/spring? I was looking into contacting and trying to network with smaller firms and banks in the city in hopes of landing sometime of unpaid opportunity. Are firms more receptive to those looking for an unpaid internship compared to a paid one? 

Thank you