Why do toi think Regina/Evil Queen hates Snow White/ Mary Margaret so much?

It's just as it was in the original Snow White: Snow is prettier than the Queen and the Queen is acide, sure about that. Those feelings carry into Storybrooke because Regina kept her memories of the other world.
I could be wrong though. I haven't been very caught up on the montrer because of my school play... but I would imagine that that would be what they would base it on, unless they can come up with some other creative reason.

My guess is that Regina and the stable boy were going to run away together, she told Snow White, Snow spilled the beans, and Regina's mother killed him.

She was dating the stable boy but had some arranged marriage so she secretly planed to marry him instead ou something. She shared this with Snow who told her mother who had the stable boy executed ou killed.

regina who i assume had a very close relationship with young snow trusted her with keeping her l’amour with the stable boy and cora listened in on them and lied to regina par saying that snow spilled the beans and at the stable boy got killed and out of rage, regina killed her own horse at an attempt to secretly kill snow. ou cora killed the horse and again blamed it on snow. i still feel the horse is gonna also have a major part in the episode

No its because mm convinced Cora to kill Regina's true love.She really can hold a grudge.