Read some of the Trent incident timelines for an idea of what happens on the naval side as not much would have changed ( still a complete curb stomp and blockade ) . Looking at the impact of a blockade you have to remember a fair bit of the sea trade of this era was actually internal US ( ie both Ports actually in the US, New York - New Orleans for instance ) not true export. Hence just looking at export/import will underestimate the effect.
Land side the US has big logistical issues as the sea and Great Lakes would be key routes for supplies. The US would still have to deploy a lot of its troops to garrison the South and protect the coast. Hence US forces deployed to Canada will not have overwhelming numbers. The quality of the US forces was not actually seen as very good. Most contemporary European sources rate most of them as only equal to second line troops ( they cite lack of training as well as the usual practice of using units till they were depleted, then disbanding and raising new ones instead of feeding replacements in ). British regulars would be rifle armed, trained to fire more rapidly and at far greater range. The supporting artillery was longer ranged and a lot of reform had happened following the Crimean War to improve logistical support and tactics.
Finally some of the imports being stopped would cripple the US military in the short term ( Nitrates for Gunpowder, quality steel for gun barrels for examples) and there would be a lot of unrest both in the South and New England which would see their economies crumble very quickly.
So possibly a bit of Canada taken before reinforcements arrive in numbers from the UK but longer term the US is brought to the table and at the very least loses its gains and has to pay compensation.
