Hi Lou and Charlotte:
Since you two are so young I think you'd have the best time in so-called "college towns" like Austin, Texas, Athens, Georgia, or Charlottesville, Virginia. These 3 are home to their respective state universities and have huge student communities. You'll certainly find vibrant new music and art scenes there. The Dave Mathews Band comes to mind as a band that grew up in Charlottesville, for example.
Asheville, North Carolina is another fun town even though their local university is a little smaller than the others.
Because Austin, Athens, Asheville and Charlottesville (especially for you Charlotte!) are located in southern states they're going to be cozy warm during the winter months. That being said however, I think some of the posters here over-emphasize the severity of the cold in the northern states. New York will be colder than you're used to in Cornwall, but the real severe cold stays pretty much in the north-central states such as Wisconsin, Minnesota and around. Montana is an interesting idea because it is so remote and wild but it will be VERY cold up there in January. Missoula and Bozeman are the prettiest cities in that state, IMO, and are also the seats for the state universities up there.
Halloween is becoming more and more popular every year. San Francisco has the wildest Halloween parties anywhere, but it also gets crazy in any good college town.
Thanksgiving is really for families in the US, so you need to get to know someone so you can be invited to their Thanksgiving dinner! Otherwise it will be a very quiet day for the 2 of you.
Everyone talks about how magical New York is at Christmastime and it's true. New Year's Eve in Times Square would be unforgettable. You might have snow in New York at Christmas; but you might not. If you want to be sure of snow try the mountains of New Mexico, Colorado, Utah, or Montana (as the earlier poster mentioned).
January and February might be a good time to go to the desert southwest -- Arizona and California. February is about the only time of year you can see the Grand Canyon without crowds.
Don't give up on air travel as an efficient way to get around. With a few weeks advance booking you can take a flight from Texas to New York for as little as $99 each way. The same trip by train, bus or car would take up to 3 days and would end up costing you almost as much in incidentals. Even the smaller cities in the US have airports so you don't have to travel to a large city to get a flight with good connections.
Good luck with everything.