Are you sure he killed her and not that, after she died of some other reason, began to scavenge and eat her? From what it sounds like, he did kill her, but since you didn't see it, you should consider all possibilities. Of course, you don't want to keep a cannibalistic bird. I'm not saying that. I'm just saying check the health of your birds for any other cause of death. You want to make sure there is nothing contagious.
The point Kherome brought up about the white birds being pecked more is true. It's because blood, dirt, and anything else unusual and attention-grabbing is easy to see, so the quail peck at it to investigate, which prompts more pecking until it escalates to violence. A dark colored quail is naturally speckled, and any dirt or blood won't grab other birds' attentions.
In pheasants, cannibalism happens when the birds are starving for protein. Are you feeding them chicken feed? Switch to turkey or gamebird for a while. That has the protein that will satisfy their appetite- if this was the cause and not simple aggression.
As far as the cold being a factor, I don't think so- unless maybe the hen was cold, so she kept piling up on the roo, which eventually annoyed him so much he attacked her? I'm not familiar with Celsius, so I couldn't say whether that is too cold for quail to take or not.
Hope I gave you something(s) to consider.
Sorry about the hen though. I'm told (I have no A&M) that when there is mixed company the white birds get pecked the most. Not sure if it is true, but it is worth noting.
