Harry might be initially shocked and embarrassed. A Howler is a very public form of scolding, and in front of all his friends and classmates, it would be a humiliating experience for him.
Voldemort might initially be furious. He's not used to being challenged in such a blatant way. He could try to destroy the Howler immediately in a fit of rage.
One possible reason could be that Harry has made a significant mistake in Potions class. Maybe he has endangered himself or others during an experiment, and Snape, being strict about safety and proper procedure, sends the Howler as a very public scolding.
The Howler might contain Harry's anger and defiance. He could be yelling about all the harm Voldemort has caused, like the deaths of his parents and many others. It could also include threats of how Harry will stop him once and for all.
Well, it could be that Harry sends a Howler to the Ministry of Magic. He might be frustrated with their inaction or wrong decisions regarding the safety of Hogwarts. The Howler could expose some of their secrets or simply be a very public outburst of Harry's dissatisfaction, leading to a big political mess within the wizarding world.
It could lead to all sorts of chaos! Maybe Voldemort is furious and retaliates immediately.
Perhaps it leads to a confrontation between Harry and the fans, or it could inspire a change in the way the fans view Harry or Voldemort. Maybe it even sets off a chain of events that affects the entire magical world in the fanfiction.
He might be initially embarrassed, especially if he receives it in a public place like the Great Hall.
Harry would probably be very confused at first. He's so used to Snape's animosity towards him that when Snape forgets who he is, it would be a complete shock. He might also be a bit suspicious, thinking it's some sort of trick. But as time goes on, he could start to feel a bit of pity for Snape, especially if Snape seems lost or confused without his memories of Harry.
It could be Professor Snape. He often had a contentious relationship with Harry, and if Harry did something that Snape thought was particularly wrong or against school rules in a way that affected Snape's interests, he might send a Howler.
Snape could initially be skeptical. Given their long - standing enmity, he might not believe that Harry's apology is sincere at first. He might respond with a cold glare or a sarcastic comment, like 'Potter, your apologies are as empty as your head.'