Why does my night HDR image show so much noise in the sky?

Firstly it's essential to distinguish between HDR imaging and tonemapping. You produce a high dynamic range image from multiple exposures, but then in order to display the result on a typical low dynamic range monitor you need to convert it down to a low dynamic range image. This step is known as tonemapping, and is generally responsible for the "HDR look".

Secondly dynamic range is inversely proportional to the image noise floor. It's the difference between the brightest thing you can capture, and the point at which detail is lost to noise in the shadows. Thus if you have very little noise, you gain extra detail in the shadow and thus have higher dynamic range.

You can tonemap from either high dynamic range or low dynamic range images (the latter is sometimes referred to as "single image HDR" or "fake HDR"). The only difference is that if you try and tonemap an image with low dynamic range (hence higher noise) this noise will become very apparent in the output.

Fundamentally the problem here is that the dynamic range of your scene is far too large. Think about what you're photographing, the bright areas of the ice are lit by intense floodlights. What about the shadow areas of the image? They're lit by reflected light (after bouncing multiple times), distant man-made ambient light, moonlight and starlight etc.

The point is the dynamic range is huge between the ice and the dark areas. So the dyanamic range of your original blend is not high enough, hence you have excess noise in the tonemapped result by the processes described above. Essentially tonemapping is trying to even out the brightness where that simply isn't practical.

Even if you expanded the range of intital captures you'd still have difficulties with bloom and flare when trying to image dark regions next to extremely bright ones. Personally I'd forget about trying to shoot tonemapped HDR in these situations - I think your original image looks fine.