Although very likely that she did, to me it makes more sense that he died suddenly and unexpectedly. While he was alive the Evil Queen was convinced she was the most beautiful. He died and she thrust Snow White into servitude or just dismissed and didn't take care of her. When Snow White started to mature and draw outside attention the Evil Queen then decided to take action against her (plus the whole fairest of them all). If the Evil Queen had killed the King why not kill Snow the same time too. Blame it on an epidemic sweeping the castle.

I always had this idea that she didn't directly kill him per se, but he fell ill or got wounded and she might've been in a position where, if she'd taken proper care of him, it would have increased his chances of survival. I think that she was not the cause of whatever it was that he suffered from, but she might have been able to save his life if she cared enough to and put the effort in.

maybe she poisoned him or something