It would have been very much a railroad and waterway war. Roads that existed sucked totally and would not have been able to support much in the way of logistics moving north (for the Americans) or south for the Canadian/UK side. I'd suggest that the defense would have the advantage there.
That said, Canadian transportation would be limited to the railroads running east & west along the Great Lakes within reach of American attacks (think War of 1812). While the US Army was small, it was pretty good for its size and while the bulk of the US militia/National Guard was pretty bad, quantity has a quality of its own and it could concentrate large numbers by rail fairly quickly (think the 1916 events in Texas and the southwest).
The weather would have been brutal, both on land and at sea, and had a major impact on transportation and supply lines.
Who could control the Great Lakes I think would have had the advantage.
As to naval combat, I'd guess that the UK would have had the same issues that the US did when it proposed sailing its battleships to fight the Japanese navy. No navy of the time had any sort of decent LOG ability to refuel and resupply at sea. The US would have an advantage in oil (Texas), but no "Big Inch" pipeline at the time so totally dependent on coastal shipping, while the UK would have had a hard time to move its supply across the ocean to the ports and ships there (did not most of the UK's oil come from the US at the time?).
US coastal defenses were pretty good and land based aircraft, even in their 1930's guise, would have been a serious threat to the UK navy, so I'm not sure that there would have been much going on in that area.
If one thinks that the UK could have gotten Mexican involvement (with what?), how about the US messing about with the Irish (it was only a few years after the creation of the Republic) to seize the rest of the island?
I'd suggest that using it as a background for naval games might be of use, but the rest of it would be a bore and not all that interesting.
Dan