Not sure if I agree with the OP that this [edit] can't be improved by playing. When I first took an interest to chess I remember having to try very hard to visualize 2-3 ply ahead. Many times after 2 or 3 ply I'd get confused and have to start over... after a few tries if I finally did it I was very happy! Other times it was too hard and I'd just have to wing it heh. 8 years later I don't have this problem
Also when studying from a book, play the moves in your head from the diagram as far as you can before using a board, then go ahead and follow along on the board to see how correct your image was. After awhile you won't need a board (if the variations aren't too long or complicated anyway). Could probably be paired with fromper's idea, when playing over the master game many times, start to read two-three moves, then look at board, visualize them, and play all three in succession.
Playing more games definitely helps with visualization, as long as you're playing slow and not moving pieces on a board (in "turn based"/correspondence style play). After all, in slow games, most of what you're doing is trying to picture what's going to happen next.
I like the idea of trying to visualize as far ahead as possible while studying books. Usually, when I read a book, I'll move the pieces on a study board for the main lines I'm looking at, and only try to visualize without moving things when I get to sidelines in the notes of the main line. At least, that's how I read a book on the first pass. The second time through the same material, I'll often play out the sidelines on the board, too, or at least the ones that seem important. I think I will try reading with more of an eye towards trying to visualize without moving the pieces - right now, working on my visualization skill is probably more important than getting through the material in any chess book, anyway.
I have realized I was short on position evaluation skills (reading the board). This meant there were simply too many possible moves I might make and the visualization thing became just too much. I recently purchased Silman's Amateur's Mind and now Grooten's Chess Strategy for Club Players. What has happened is deciding on the best move is becoming easier (sometimes) and with that I have more confidence and mental energy to spend on the visualization. The two (Best move and visualisation) combined, make the overall process easier and thus it has been a helpful and important development for me.