To re-emphasize, cadre cannot open basics mail and read it. However, if there i writing visible on the outside (like a postcard), there is nothing keeping anyone from reading it. Some cadre have basics open their mail and show it to them, but that is to ensure no contraband is inside. Some cadre are okay with pictures printed on the paper, others are not. Some cadre (like when I worked), it depended on the day and how I was feeling. Some times I'd feel the envelopes and let it be, other times I was more strict. Other days I just wouldn't take them to get mail.
But another thing to stress, WRITE YOUR BASIC EVERY DAY!!! It may seem old and that you don't have much to say, and no they don't have a lot of time to read novels, but getting a quick "hello, hang in there, we're thinking of you" means so much. If you haven't, address envelopes to your basic and give them to his/her friends so they will be more likely to send it