I do believe that the TOR network uses encryption. When data travels from your computer to a TOR node (or from one node to another), that data gets encrypted, so that it can only be decrypted by either the user or the "exit" node (that is, the last node between you and the web). Therefore, using TOR while connected via public hotspots should help protect you from this garbage.
PS: I can't help but wonder if these ads also affect HTTPS traffic as well. If so, it seems likely that this advertising will have the same effect on privacy and security as the Lenovo Super Fish fiasco.