No, in itself that's OK. The problem is the abuse that you describe.
Yes, but given human / corporate nature, when the system is set up to make abuses easy, they are guaranteed to happen. So given the way the system works today, allowing a trademark on "winter is coming" is in itself problematic because it invites abuse. To avoid the abuse, the trademark system needs to be reformed in some way, whether that's to make it easier to dismiss invalid lawsuits, harder to get stupid trademarks, or something else.
As a good incentive, this incentivizes not doubling down. Rather than issuing a non-apology apology with only minor changes at the top of the story, thus spreading a badly flawed story further, it incentivizes either correcting story in-line or removing the story entirely, with only an apology in its place.
I disagree, I think it incentivizes completely deleting the story and replacing it with nothing. That's clearly the safest option after this ruling.
Intentionally selling something by deceiving the buyer into thinking they are buying something else is already illegal.
That's not what this is. The only thing being sold is advertising, and that part probably isn't fraudulent. We'd have to see the actual contract but I doubt it says anything about the veracity of the content. The reader isn't buying anything, so there's no fraud there. Just lies.
No, I disagree. There's nothing wrong with such a trademark.
There is something very wrong with such a trademark, because now any time anyone wants to use the phrase "winter is coming" in a work of fiction they are at risk of legal action from HBO. They have taken a normal part of the English language and claimed it as their own.