If by "safe" you mean "my sexting pics will be deleted after 10 seconds". Your Snapchat buddy can just take screenshots*, or use another camera to photograph the screen of their phone. Then it's just a matter of time until your Mom, your school and your friends... you get the idea.
Although Snapchat messages are designed to disappear in 10 seconds or less, there is no guarantee that the recipient won't take a picture of the message using the "screenshot" feature of their phone or by taking a picture with a camera.
Snapchat attempts to detect when recipients take a screenshot and sends a notification to the sender, but even this is not fool-proof.
As with any online service, one should always "Think Before You Send" and consider the trustworthiness of the intended recipient(s) before choosing to share an image or video with them - if it's too sensitive to risk someone else seeing it, then it shouldn't be sent!
If you really want to show horny4u1998 your private parts, consider whether you'd post them on Facebook to your friends first. If not... don't even take the picture.
ps: come play my premier league score prediction game - guaranteed safe!
* sure, Snapchat tries to detect this and send you a message but... your (presumably ex-) buddy still has your naked pix.