Won't having disk shaped wheels cause more wind resistance with crosswinds? What are the benefits of having these sort of wheels?
Disc wheels have lower drag than spoke wheels. See Wheelbuilder aerodynamic data and Aerodynamics of High Performance Race Bicycle Wheels. (One link shows simulated data, the other measured).
Most of these tests run up to yaw angles of 30 degrees. The argument is typically that at higher yaw angles (closer to side-winds) the rider would choose a spoked wheel instead of a disc.
Disc wheels are typically preferred for courses and days that do not see a lot of cross-winds not because of drag, but because they present a large area for the wind to push on, and can lead to unpredictable performance in high-crosswinds. This is one reason you don't often see disc front wheels in a non-velodrome environment.
I found a link here: http://www.wing-light.de/CFD/wheels.htm but you can also get similar graphs from manufacturer. It shows different amount of drag in different wind angle.
Crosswinds don't necessarily give high drag, obviously it should give lower drag than headwinds. Even when it's directly blowing from the sides, depending on the speed of the bike and the wind, the resultant angle is not 90 degree.
Now, here's the interesting part, if you check the graph, at around 20 degree angle the disc actually has negative drag! I reckon to get that kind of angle, you need a higher degree angle (more like crosswinds) when you're moving fast.
The benefit of a disc wheel is that you can ride faster than with a spoked wheel, on flat and rolling roads and at steady speeds. Once hills (gravity and lower speeds) or changes of pace, come into the mix the case for spoked wheels becomes stronger.
I learned in physics class that solid wheels have a lower moment of inertia because the center of mass of the material is located closer to the hub (think of a skater holder her arms in and spinning). Technically, this should make the wheel easier to accelerate and lower the resistance of spinning the wheel. The do weigh more, so is this of any advantage and a reason for having them?