Snapedom

I kept waffling back and forth as to whether he went to school or not, but I think I agree with Nemesister. Young Severus seems so poorly socialized that it's unlikely that he spent much time around other children.

However, to try and split the difference between the two choices, I'll say that maybe he went to a Muggle school for a short time--perhaps at Tobias's insistence, against Eileen's wishes. But he began doing spontaneous magic, much as Harry did--maybe in reaction to being bullied by the other kids, and his parents hastily took him out of school, and Eileen home-schooled him from then on. He wouldn't have spent long enough at school to be properly socialized, and it would have demonstrated to him that he could never fit in with the Muggles. Also, at this point, Tobias may have washed his hands of his son, realizing that Severus will never be "normal," and maybe it is at this point that the neglect of Severus begins and the fighting between his parents escalates.