Instead of a full hiking boot you can also consider getting a hiking shoe but still with a steel shank for support. Something like this for example:

Merrell Sidestep hiking shoes
http://www.ems.com/product/index.jsp?productId=3652480

These shoes will be much lighter and smaller to pack than a true hiking boot which may not be all that useful for much of your trip.

Depending on how groomed the trail is you can also get away with something more urban which usually involves a more flexible sole. Like this:

Merrell Moab Gore-Tex XCR Cross-Training Shoes:
http://www.rei.com/product/757560

These are also waterproof which will be nice if you're walking through snow. Of course, pair with gaiters depending on how deep the snow is. These shoes will also be great for general touristing as they're lighter and the sole will flex more which makes it less fatiguing to walk on level surfaces. As an added bonus they have speed laces for clearing TSA checkpoints.

For traction on ice Yaktrax Pro are great and can be carried in your pack while not in use. The top strap keeps them more securely on the shoes than the ones that only surround the sole. Do not EVER walk on a hard smooth floor with these (marble, stone, etc.). You will only make that mistake once though if you forget. Concrete sidewalks are ok.
http://www.ems.com/product/index.jsp?productId=3667582