Promote climate change perhaps? Put her in conflict with Mab, maybe? By that if she can get around easier, Mother Winter might overrule Mab, and that might not be good.. Here is a thought, it was Mab who originally stole or arranged for Mother Winter's walking stick to be stolen in the first place. It was part of a power grab, and somehow handed it off to the White Council to deflect suspicion from herself..
I think the division of power and jurisdiction is pretty ingrained between the Queens. They'd pretty much have to be nemfected to try to circumvent the proper boundaries between them.
Perhaps Mother Winter wouldn't overrule Mab as much as get in the way; and, or cause confusion with other powers about who was running Winter's affairs. The later situation might actually threaten to weaken Mab even if Mother Winter wasn't actually trying to overrule Mab. Even a couple centuries ago Mab knew that the major test of her reign was in front of her; and from her perspective was right around the corner, so I think anything that might threaten Mab's image of leadership and control would be something she would especially proactive dealing with.
So Mab being responsible for the theft of Mother Winter's walking stick seems like a reasonable guess to me. Of course, Mab wouldn't have taken it herself. Harry once said that Martin probably didn't plan on wiping out the Red Court with the bloodline curse; that was just one of a range of possibilities he foresaw, but when the opportunity for the Red Court's complete annihilation presented itself, he went for it. Something similar may have been going on with Mab. Mab may have been looking for a way to diminish Mother Winter and firmly assert her own leadership of Winter, saw the opportunity and made certain someone from the White Council knew where and when MW's walking stick would be vulnerable.
(Here's something that I don't believe has been stated in the books or by a WoJ. How long has the White Council had the Blackstaff? Now that I think about it, Ebenezer made it sound like the Council had control of it for hundreds of years or even a thousand years. Maybe Mab hobbled Mother Winter early in her reign in order to assert her dominance so no one would doubt who the new boss was.)