I just loaded it up.  My observations:

You've got an extreme range from light to dark, but the exposure is perfect.
You couldn't have exposed much higher without blowing some detail.

There is chroma noise in the deep shadow areas in the left bottom corner
and on the right side in the trees and mountain; I assume that's what you
were talking about initially.  I don't think there was any way to avoid it
in a single exposure given how dark those areas are -- it's just the noise
characteristic of the camera.  However, taking "color noise reduction" up
to 5 in Adobe Camera Raw eliminates it with no negative effect on the
picture.  Non-issue.

There is chromatic aberration in the high-contrast edges, in particular on
the right side near the sky and on the lower left in the sunlit snow.  The
red/cyan CA slider in ACR takes care of it; I swooped it over to about -40
and that looks good, at least as a start.

There is posterization in the shadows, noticeable in for example the rocks
on the lower left.  That's the nature of digital shadows, and could only
be avoided with more exposure, which you couldn't really do in a single
exposure without a graduated ND filter (which would have been tricky
given the composition).  Just let it go; while it was slightly noticeable
at screen resolution, I tweaked the curve a tiny bit on the shadow end to
darken the shadows a bit and you'd never notice.  You can still see the
artifacts of it at 100%, but really, no big deal.

Don't bother trying to boost the shadows.  It will bring out the problems
and I don't think it's necessary -- it reduces the overall visual contrast
and (in my opinion, we're getting into aesthetics here so take it for what
it's worth) detracts from the picture.  In fact, I think darkening the
shadows a bit as I described above improves the impact.

To get really good detail in those shadows, even with a "better" camera,
would require more exposure, possibly using multiple exposures and the
Merge to HDR function in Photoshop.  Yes, a "better" camera would have
had less chroma noise there, but the noise you have is really just not
anything to worry about.

In short -- I think there is nothing technically wrong with this picture
that isn't quickly solved with simple processing.  In addition to what I've
described, if it were mine, I'd probably take it into Photoshop proper and
try to increase local contrast in the sunlit mountain, but all in all, I
think you might be falling into the pixel-peeing trap.

If you shot this (and similar pictures) on a tripod, consider using auto-
bracketing to take a series of exposures, starting with where you were at
and then overexposing by a couple of stops, and playing with Merge to HDR
in Photoshop.  That takes a bit of learning, but if you want better detail
in those shadows that's how you'll get it.

That scene, as other have already said, has tremendous dynamic range.
Your mountain-top snow in the sun is slightly clipped in the RAW data
(most of it is clipped in the green channel, less in the blue, and even
less in the red, as you'd expect with snow in sunlight).  Besides the
snowcaps, the next brightest thing in the RAW file is over a stop darker
than it, so, even though you have achieved an "exposure to the right"
with very little clipping, the only thing you would have lost by
exposing a stop higher would be a little detail at the darker edges of
the sunlit snow.  Since the snow is such a smaller feature of the
overall image, I would have let it go clipped, for the shadows' sake, if
I wanted the shadows.