I'm pretty sure this is done at a large scale in both Norway, Sweden and Switzerland. While storing energy have always been a huge problem, I'm surprised this is not more popular.
This is correct. Norway exports power in wet seasons, and imports it in dry seasons. But if there is less rain and dam fill-up than expected, they will throttle down on production to save the water in order to sell it at a higher price later on.
AFAIR it's done in italy too (~1/5 of the national power is hydroelectric) and I am reasonably sure all the big plants work with dams/reservoirs, e.g. http://en.wikipedia.org/wiki/Entracque_Power_Plant
Well it needs a lot of water (which can be problematic for the areas which solar is most competitive in) and a lot of unused area. It's a very reasonable solution when you meet those constraints though.
France built out a system of hydro dams and nuclear power plants in the 70s, and they store excess nuclear power by pumping from reservoirs downstream to ones upstream, for later hydro power generation. Unlike Denmark, however, France has the Alps, and thus a suitable location for dams.
Seems like an ideal arrangement would be to use Norwegian hydro power installations as a buffer for Danish wind power output.
I find the idea of using a dam as a battery quite interesting.