Travelling across the USA?

Of course it is possible. Many people have walked across the US: http://en.wikipedia.org/wiki/List_of_people_who_ha... using various routes. The best route would take quite a bit of research. If you are traveling in the winter you would probably want to walk south of New York (rather than going east) and stay near the coast to avoid winter weather, especially winter weather in the Appalachian mountains.

You can't walk along the edge of most interstate highways, but walking as close to highways as possible would probably be the easiest. For example, following I-95 from New York to near Richmond, VA and then going along several highways to Charlotte, NC and from there following along near I-20 across the country. Here is a google map with a possible route: http://goo.gl/maps/AXWZE

As for how long it would take - that depends on the person walking it. It is over 2500 - 3000 miles (4,000 to 5,000 kilometers) Can you walk 20 miles a day, 30? or ? Do you want to stop and look at things or just keep walking? The google estimate is about 1,000 hours of walking so if you walk 25 miles per day it would take 40 days without allowing for any additional time for rest days, side-trips or sightseeing. Most people who have walked across the US took quite a bit longer - most at least 80 to 100 days and it has taken several people months or years to complete the trip depending on their purpose for doing it.

The average speed a healthy vibrant person walks is between 3-5 mph. Let's call it 4 mph. Champion speed walkers hit over 8mph.

In 10 hours of walking you could cover 40 miles. I reckon you'd get faster over the course of the trek as well.

Assume you want to start at the Atlantic Ocean and finish at the Pacific Ocean. For a winter trek I'd start in Jacksonville Florida and go strait west.

If you start in NY you would either need to walk south for a long way before turning west or face some nasty weather if you don't. The most snowfall in the US historically happens in upstate NY, cold Canadian wind blowing over the great lakes makes copious amounts of snow. I wouldn't want to walk face first into the wind either. Then when you get towards the mountain states you'd be faced with crossing the Rocky Mountains. You could go across southern Wyoming, which isn't super mountainous but the distances between civilized places is pretty vast out there and Wyoming is notorious for savage wind in the winter months (I grew up just south of the Colorado, Wyoming boarder) the kind of wind that blows over large trucks going down the road. So start in Jacksonville.

The distance Jacksonville to LA is roughly 2400 miles / 40 miles per day = 60 days of walking.

Keep in mind you can only stay in the US for 90 days on a tourist visa.