Filesystems typically do not store time zone information. Good filesystems (e.g. Linux's ext2/3/4, BSD's ffs, Windows' NTFS) are defined to store all dates in UTC, i.e. as abstract instant in the conventional reference time scale; conversion to local time is done when reading the metadata from the filesystem and displaying it to the user. Bad filesystems (e.g. FAT) store dates in "local time", whatever the local time is at the time of writing, and do not contain any field indicating what the current time zone is. So FAT does not indicate the time zone of the machine which wrote the file, but you actually need to know that time zone from some other source if you want to make sense of the timestamps in the filesystem.
Some archive formats (e.g. tar, very common in the Unix world) will record some timestamps, but they copy it from the filesystem, so they are as timezone-less as the timestamps in the filesystem.
This is a rather generic way of computing things. A time zone is a way to interpret an "instant" (in the common time scale) into a "local time". In countries which practice daylight saving time, computers switch time zones twice per year, making usage of local time a bit delicate (people get away with it because the switch happens when they sleep, and they are officially requested to behave as if the switch never happened; but for computers, this is bad: they don't like it that "October 27th, 2013, 02:30" ambiguously designates two instants in Europe). Thus, when computers are aware of time zones, they internally compute with UTC and convert to "local time" only when it comes to talking to humans. Therefore, filesystems and other data storage systems tend to store dates as UTC. The "current time zone" is a fleeting information which is subject to change, hence not written. Local time is stored only by systems which are not aware of time zones (they know only of one time scale, which they assume to be meaningful to the human user), and these systems, of course, cannot write down their current time zone, since they don't know it.
Note that some information can be written in other places. For instance, digital cameras will produce image files with a lot of metadata information (using the EXIF format) and will do their best to indicate the exact geographical position of the camera at the time the picture was shot. In particular, if the camera contains a GPS receiver (as is typical of modern smartphones), it will pinpoint the camera within a few meters, which is a lot more accurate than simply knowing the time zone (a time zone is as precise as "somewhere in Europe").