The Detroit Red Wings winning the Stanley Cup over the Carolina Hurricanes was a definite victory for Detroit. Likewise, the Republicans winning control in the House and the Senate was a victory for the Republicans. For a person, or group, to be victorious, they must win the battle and have no question as to who won; the winner must be obvious. Referring to this definition, the United States can not be considered the winners of the War of 1812 because of the Treaty of Ghent in 1814, the Battle of New Orleans in 1815 and the Hartford Convention, also in 1815.
In 1814, Britain demanded that the United States give up naval forces on the Great Lakes. They also wanted navigation rights on the Mississippi River and permanent ownership of Fort Niagara and Sackets Harbor, along with several other things. America would not hear of any of these and they had some conditions of their own. They wanted Britain to end impressment, pay compensation for the ships that they had seized and follow international blockade rules. Both America and Britain eventually lightened their demands and as a result the Treaty of Ghent was signed. The Treaty of Ghent ended hostilities and restored pre-war conditions.
The battle that was not supposed to happen in the first place was the Battle of New Orleans. The U.S. did not receive word of the Treaty for nearly two months and in that time frame, the Battle took place. Even though America won that battle, the war had already technically been over so it's not possible to say if it contributed to the winning of the war.
The Hartford Convention may not have a step forward for Americans had it gone through. It was made of mainly Federalists who were said to have "formulated demands that amounted to a dissolution of the Union." On February 13, 1815, the secretary of state was handed a copy of the Treaty of Ghent and thus ended the Hartford Convention and the Federalist party. This was not a clear-cut win in the war for America or Britain.