I didn't see a thread for him so I thought I would make one.
We know that Snape's father and mother were always arguing and he didn't like magic. However we don't know the extent of Severus and his fathers relationship. Do you think it would be in character for Tobias to drink and hit his son?
Beset by Owls
Well, I don't think there's much evidence against it, so I think it would be up to you and how you want to portray the relationship. In the Prince's Tale snape says about his father:
"He doesn't like anything much."
That seems to indicate that at least Snape himself doesn't feel liked, or even less; loved, by his father. He also starts tearing leaves apart "apparently unaware of what he was doing." He clearly has very (perhaps supressed) negative feelings about his father. The fact that he according to Snape "doesn't like anything much" makes him appear to be a very disillusioned and misanthropic man.
But when Lily asks how things are at his house, he says "fine", which could be a sign of him not wanting to betray his family and that is as far as I know pretty common among victims of domestic violence.
When Harry enters his mind in Seen and Unforseen in OotP he sees what he presumes to be Snape's father and mother; the father is shouting at "cowering woman, while a small dark-haired boy cried in a corner." That fact Snape's mother is described as cowering does not make it look like she was the arguing type really, it more seems like her husband was verbally abusing her, at least on that occasion, and that (to me) makes the possibility of him being physically abusive as well not too far-fetched.
I've always seen Tobias as quite a violent person. If we assume that the arguing people Harry sees in OotP are in fact Severus's parents, then we face the idea that a Muggle is making a witch cower. This, in itself, seems to suggest violence in the household. Eileen, being a witch, could have hexed him. The fact that she didn't means one of three things.
1. There was more to the memory - perhaps Eileen hexed Tobias outside the parameters of what Harry saw.
2. Eileen didn't see herself as in danger - Tobias may have been all bark and no bite, however Eileen's 'cowering' seems to refute this.
3. Eileen was too scared to use magic, or could not use magic - Perhaps Tobias had taken her wand, or Eileen wasn't particularly good at DADA, or she may have been scared that Tobias would beat her more severely if she tried to use magic. Or maybe she had even lived in the Muggle world so long that magic no longer came automatically to her.
If we agree with scenario 1, then Tobias could have merely been bitter from being excluded from so much of his son's, and wife's lives, or completely under the control of Eileen, who with her magic would have been more powerful.
If we agree with scenario 2, then Tobias seems likely to have been a slightly abusive drunk - many do say things they regret later on, and outside of that memory may have been a completely well adjusted person.
If we agree with scenario 3, then Tobias would have very likely been abusive and violent towards his wife, which may have translated over to his son.
Also, taking in the fact that as a young adult Severus took the Dark Mark, and joined a predominately Muggle-hating group it seems likely that he and his father did not get on, and that Severus (at least at the time) hated his father. This could have come from living in a home where domestic abuse was a regular occurrence.