The haze is a result of the size of your terrain. Really long view distances over large terrains naturally should have more haze (think of looking from the top of a very tall mountain into the distance - everything fades away in the haze).
The problem here seems to be that TerreSculptor doesn't export TER files with correct scaling values. I created a 2048x2048 terrain and it came in 261 km to a side! That's *huge*, it's about the length of the entire coastline of Washington State in the US. Not only does this make things hazy, but it also messes up the relative slope of things since the heights get stretched over a larger area and thus appear less steep and dramatic (quite flat, in fact).
Fortunately the solution is quite simple, although not exact. Just go to the Terrain Layout, then select your Heightfield Shader in the Node List on the left, and click the Add Operator button at the bottom of the Node List. Select Heightfield Resize from the list of options. Now go to the settings of the Heightfield Resize, make sure Re-size In Metres is checked (and not Re-sample Pixels), and then adjust the values for the Resize in Metres. It defaults to 10,000, but I found about 40,000 (for both sides, since it's square) looked good. Note that you want to keep Re-Scale Vertical *unchecked* because the vertical scale appears to come in more or less correctly, it's just the horizontal scales that are messed up.
I did actually notice that even the vertical scales may be a bit odd, with both positive and negative displacement in my case, but that may just be how I created by simple test terrain. I would assume the vertical heights are correct, at least to start. You can always add a Heightfield Adjust Vertical to experiment with that later. But I don't think you'll ever want to use the Re-Scale Vertical checkbox in the Heightfield Resize because you'll just end up with the same flat look to your terrain as you had originally, and with no additional control to decide just how high it should be (which the Heightfield Adjust Vertical gives you).
Edit: Ah, Bobby beat me to it.

- Oshyan