Effect of noise on high and low frequency components
This is actually due to the characteristics of the actual signal, rather than noise.

You might have heard of pink noise and its spectral characteristics $$S(f)\propto \frac{1}{f^\alpha}$$
Now forget about the term "noise" in here, and imagine a stochastic process whose spectral density vanishes following a $\frac{1}{f^\alpha}$ law, in which $\alpha$ is a constant.

Interestingly, this is the law that nature follows a lot. More specifically, many natural signals follow this law. It has been observed and actually been verified to be valid for instance in human voice, natural images, music, quasar light emissions, heart beat, firings of neurons, and even in financial markets. Note that natural is a key term here and by that, we refer to attributes of a natural environment. For a more detailed discussion see here and here. For 2D (image) signals we should expect $\alpha=2$. 

Since according to the $\frac{1}{f}$ law the contribution of the actual [natural] signal will diminish at higher frequencies, we would expect more contribution of noise at these frequencies. Consequently, noise is usually dominant at high frequencies and the signal is more dominant at lower frequencies.