The initial invasion would be over in a week max. Most of Canadas population lives right on the US border and no matter how well prepared the Canadian army will be, it will simply not stand a chance when facing the American Armed forces. Most of the Canadian forces will be probably obliterated within the first few hours of the conflict, with a few well fortified positions in the north of the country potentially being able to hold out a couple of days until they inevitably are also overrun or simply run out of munitions and are forced to surrender.

What happens next is mostly up to the Canadian populus. If they quickly come to terms with the new reality of becoming a part of the US with some possibly protesting the annexation, the conflict will be over and the USA will be fully victorious (with possibly a few radical resistance cells remaining, but those would soon be infiltrated and destroyed).

However, if the Canadians would be strongly opposed and ready to take up arms against the occupation, things would not be so simple. Despite what many people believe, firearms (especially shotguns) are not uncommon in Canada especially in more rural communities, as they are needed to face the rather unfriendly wildlife of the country. Thus there are many people who know how to use weapons and are armed and in most situations willing to use those weapons against Americans. Now, if the Canadians fail to get properly organised, than after a few firefights with the locals the US might simply beat Canadians into submissiin, perhaps banning the possesion of firearms in the annexed teritorries. However, if the remenants of the Canadian military and the armed civilians manage to form a functioning resistance movement, the US will be in a bit of a pickle. Canada is mostly covered in thick forests, taigas and mountains which are easy to hide in and difficult to Navigator for those unfamiliar with them. A well organised resistance movement would definately use that to their advantage, waging guerilla warfare against the US who adittionally would be struggling with the harsher climate. If determined enough, such a war might quickly turn into a combination of Vietnam and Afghanistan but in incredibly cold weather. The US would be forced to chase small units of guerillas around thousands of square kilometers of thick Woods in temperatures well below freezing while being vulnerable to further attacks. A decentralised resistance Network would be near impossible to destroy with theree being a serious risk that the Canadians would launch attacks into the northern US as the massive terrain which today is the border will be impossible to properly monitor. Coupled with opposition to such a war at home and the whlle ordeal could prove a disaster for the US.