Apparently the UV maps I've set in the file are still kept, but changing drive letter requires just a re-loading of the texture.
My horse would not start with the mane / tail hair texture until I've reloaded it, and as soon as I've loaded the texture, everything else just updated (transparency and specular).
Although I am not sure if this counts as if it were transported to another machine, but my hdds' drive letters are switched around anyway...
To be more exact, I have a dual boot system, and the horse was made while I was on on Win XP, but I am editing the horse on W7 and my drive D: (where the horse project is) became drive C: and my drive C: became drive A:.