So hypothetically speaking, let's say Snape would've had a daughter he didn't know about (yes canon totally unlikely he'd have a one night stand but let's pretend). Now let's supposed Dumbledore would've found out, during Harry's 4th year, Sev had a child around the age of Potter. Would he have told Snape about his child or would he have kept her a secret thinking it would distract Snape from his duties?
Dumbledore would absolutely hide a child from Severus. He would, however, justify the hell out of that decision.
First of all, Severus is not at all equipped to care for a child, especially as a full-time parent. He’s not emotionally mature enough, nor does he have the support he’d need to care for someone like that.
Secondly, if possible, Dumbledore would have figured out some way to send said child far away. Either to France or maybe even America. Anything to keep her from becoming an a liability in his war-games.
Thirdly, I think Dumbledore wouldn’t be completely heartless about it. He’d set up some clever plan about revealing Severus’ daughter to him after the war was over- maybe some sort of spelled parchment that wouldn’t open until Voldemort was dead or something.
There is a really interesting story by Arinus called Always in Your Shadow about Snape having a daughter slightly older than Harry with Bellatrix (I know, it’s gross to imagine, but it works as a story and the characters are written very well). I imagine Snape as a father to be quite a lot like how he’s portrayed in the story, though I think he’s somewhat more willing to act gentle around his daughter in this story because she comes from a background of such extreme abuse (as a parent, that part was very hard to read, so FYI, there are descriptions of extreme torture and abuse in that story).