The issue with snapchat and other social sites that you share pictures/videos of yourself or others. And the only way a person can share pictures/videos of himself is by taking them on their phone or someone else doing so, which is prohibited.
Shaikh Saalih al-Fawzaan hafidhuhallah was asked:
Question:
May Allah be good to you. The questioner says: What is the ruling on taking pictures with the cellphone camera while it does not leave the cellphone?
Answer:
“All pictures are prohibited with a cellphone or other than it. The Prophet (ﷺ) prohibited pictures and cursed the picture makers and he did not make an exception. All pictures are prohibited. All their types, means, and forms, except what is due to a necessity. The Scholars have passed verdicts for its permissibility in a necessity. Yes”
So whether someone saves it or deletes it is not the real concern because it is not allowed to take the picture/video in the first place.
Added to that, we should be aware of the evil present in many of these social media sites and apps. They are platforms for much evil and corruption, even though someone may not post bad content nevertheless, they are exposed to this evil, which will affect them and misguide them. There are many celebrities, musicians, and other failures on snapchat who create their own story for people [Muslims included] to view and waste their time. They have created a window for the youth and impressionable to watch the lifestyles of the wicked ones and listen to their opinions. Of recent, the people of innovation and misguidance have starting using snapchat to spread religious advice and even pass fatawa!! So the advice for the Muslim is to avoid social media due to this evils.
Shaikh Saalih al-Fawzaan hafidhuhallah was asked:
Question:
I want from the Shaikh an advice for the sisters and brothers who participate in social media. What is your opinion on that? May Allah reward you.
Answer:
“Evils have occurred from this [social media] and as it is well-known, it has the involvement of those who are misguided, the callers to misguidance, and the callers to fitnah. So beware of this social media and do not use the cell-phone except for calling and responding [to calls]. As for taking the cell-phone [in order] to accept these messages, this nonsense, and these distractions, then this is not necessary. Evils have come from it”
And Allah Knows Best
Translated by
Faisal Ibn Abdul Qaadir Ibn Hassan
Abu Sulaymaan