Do the Canadians have to formally ask for our help, or do we just commence to kicking foreign ass automatically under existing treaties?
NATO members are required to consider an attack on one member as an attack on themselves.
It’s worth noting that Article V, meant to be a deterrant during the Cold War, was first activated after the 9/11 attacks.
So, regarding its Cold War purposes, it seems to have worked. 
In addition, if the attacker weren’t from the Western Hemisphere, the US could intervene under the Monroe Doctrine.
You guys still use that as a standing policy?
[The Critic]
James Monroe: The name’s Monroe. James Monroe, and here’s a taste of the Monroe Doctrine!"
[smacks badguy]
Woman: Oh James!
James: Welcome to the era of good feelings.
[/The Critic]
But IIRC it did have to be activated (the very next day, in fact, if the Intarnet has not led me astray.) Presumably the chain of events would go something like this: Greenlandic forces come ashore on the Ungava Peninsula, and with alarming speed capture most of the power installations, Quebec City, and are advancing down the St. Lawrence towards Montreal. NATO holds an emergency session almost immediately. The Canadian representative at the meeting asks the assistance of NATO. Then the Yankees can go start kicking ass and taking names.
Now, what would happen if (a) the Canadian representative says, “We’re dealing with the Greenlanders just fine; don’t worry about us”, or (b) nobody can be found to represent Canada at the meeting due to the sudden and total collapse of the Canadian government… Those are more interesting questions that I don’t know the answers to.
Correct me if I’m wrong, but the Monroe Doctrine is just U.S. policy, not an actual treaty. Right?
In this case, NATO would lean back and watch the carnage with great interest and contingency plans in hot stand-by, but otherwise would sit out.
In this case, NATO would hold their emergency meeting, and in the absence of any Canadian representative, decide what to do. The upshot is almost certainly that NATO would come jumping in with both feet. The US would jump in, in this situation, regardless of what NATO decided, without a doubt - Canada is too valuable a trading partner, and has too long a common border with the US, to allow anyone to mess with them.
I think Mike is close to the mark. I think that while the US might well take action on the seas to interdict air and sea transport of the attacking force we wouldn’t cross the Canadian border on land without invitiation regardless of treaty obligations as long as there was an effective Canadian government to request help.
Now if the Canadian government was, for some reason, neutralized we might well put down the invasion and attempt to re-establish some form of Canadian government without request from the north.
hmm… not COMPLETELY sure, but I do believe that (in the case of the US and Canada) the US would actually either have to ask permission, or be invited into the country before sending armed forces. How SPECIFIC that invite/permission has to be is something I don’t know.
Im also pretty sure that under conditions of failure of the state (ie, the Cdn gov collapses and no representative of parliament is in control) the US would be able to enter uninvited.
Take that with a grain of salt though, as Im too lazy to look it up. 
Legally, yeah…ask permission. In reality, however, I’ll bet that any US forces within range of the Evil Greenlander Menace would be given very loose ROE. Any attack subs in the area, and there would be several, would get a quick message that said “Good Hunting” and that would be that. 
It hasn’t ben an issue since the Cold War, but in practice the geopolitical reasons for it haven’t ended.
Why would we need permission to kick Canada’s ass? Or an excuse . . .
I don’t see any reason that wouldn’t be the case. However to take this a step further, wouldn’t it also depend on whether or not whomever is in charge and authorized to grant permission was plotting with the invaders? IOW, say the PM is a renegade more than happy to let China take over?
I suspect the real answer would be: Depends on the US-perceived threat level of the invading force being so close to our borders.
Celine Dion alone warrants a standing invitation.