Er... No feistylilredhead, they tried it twice - and beat the stuffing out of us the last time!
http://occawlonline.pearsoned.com/bookbind/pubbooks/divine5e/medialib/timeline/visuals/visuals_Military_1_3.html
Okay I maybe missing something in my memory of maritime battles, but if I remember correctly, the War of 1812 (to which you are referring) was fought on land (Canada and the US) and of course on the Great Lakes. They burned Washington true, but we took a hell of alot of their Navy down with us and they suffered some nasty land defeats in the US and in Canada - hence the reason the war was declared a stalemate, after we won the Battle of New Orleans. Hardly had the 'stufing beat out of us' I would dare to say, otherwise they might have gotten us back
hee hee
We didn't win Canada, however we got the lakes and assured America's independence once and for all.
The Hudson and Hudson Valley was the scene of one of Washingtons' greater battles as he fought to hold onto New York. As far as I remember that's the only battle the Hudson is known for .....(not saying I'm not wrong, I just really don't remember any battle of the Hudson in 1812)
As for the War of 1812 - well we declared it ...
not the British, so you had to expect them to show up somehow, I guess Canada seemed like the easiest way in