You can buy small foldable solar panels, and it's a laptop so it's not like the battery is big or heavy. I'm not sure why you'd need anything massive for a device that sips power, just take a normal laptop instead of a high end gaming one and it'll draw like 30W.
So how do small foldable solar panels that charge phones and the like work? Because I presume if they can charge a phone they can charge a laptop, given they aren't really different.
No, but they seem to be able to charge a phone, or their own internal batteries. As long as the laptop you take is one designed for long battery life I don't see it being an issue for quite some time.