That would be awesome, but it would have to be some advanced tech involved to make that happen in a small package (likely trouncing the watch itself). I know there are US companies working on micro solar cells, however they would still require a relatively large lens to pull in light, and would do a great job of heating the internal structure of the device far passed a comfortable wearable temp, and quite possibly hurt the watch circuitry itself.
With general available solar tech, an Apple watch would require one large cell to charge / power itself. Looking at the current iPod Nano (closest thing in size and potentially power to the Apple watch), it requires a 220 mAh battery to give it respectable battery life as an iPod device. I am sure with a watch, you could cut that in half, but even then, the solar panel to produce similar power levels would be ~50 -100mm square of solid / unblocked solar cells.