I think Snape's picture is definitely in the Headmaster's room. He did occupy it for a year. Maybe its something magically automatic for someone who occupied that room. Dumbledore's picture turned up there by itself I think right after he died. He was sleeping then. This theory also holds true for Umbridge's portrait not being there. She was never able to get into that room.

I would like to ask another question regarding where Snape is.

Where is Snape's body buried? Who attended the funeral? Was there a funeral?

Well now that I've asked; it looks like there's more than one question.