Large glass bottles just don't strike me as a "good idea" for hiking.
What options are there for carrying wine and preserving the flavor for a couple of days while hiking?
The key to preserving the flavor of wine is to minimize the amount of oxygen in contact with the wine. One option is to use a container which is flexible, so that you can compress it in order to remove all the air inside, leaving only the wine. Just be sure it is well sealed, so that you don’t get wine all over your backpack. There are a few manufacturers who make containers specifically designed for this purpose, for example this one or this one. I have never used them myself, but all the reviews I have seen are very positive.
Just for @Russell:
Buy boxed wines and remove the box. This leaves you with a flexible bladder containing wine with a drip-free tap. It might not be classy, but it works.
Most of the white wine boxes have a foil lined bladder, which also helps keep the wine cool (well, cooler.)