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According to this question:

What determines color -- wavelength or frequency?

It is the energy, and thus the frequency of a photon $E=hf$, that determines where it lies in the electromagnetic spectrum (for example its color). Wavelength is determined by the index of refraction of the medium it is travelling through via $λ=v/f$.

Does this mean that a photon would appear red in color regardless of how short or long its wavelength is, so long as its energy corresponds with that of red light??? Does this mean an x-ray or gamma-ray or radio wave is still what it was initially despite of a substantially different wavelength?

For example if you pass a red light through something with an extremely high $n$ such that $v=1 \times 10^{-6}\:\mathrm{m/s}$....

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Firstly, $E=hf$ is always true for electromagnetic radiation like light. In vacuum the speed of light is always $c$, so that in vacuum:

$c=\lambda f$.

In any transparent medium, other than vacuum, light slows down to $v<c$ and we define the refractive index $n$ of that medium as:

$n=\frac{c}{v}$.

With $E=hf$ and (in a medium other than vacuum) $v=\lambda f$, then:

$\large{\lambda=\frac{vh}{E}}$ and since as $v < c$, wavelength is reduced in a medium other than vacuum.

Does this mean that a photon would appear red in color regardless of how short or long its wavelength is, so long as its energy corresponds with that of red light???

Yes, the perceived colour is only affected by the energy of the light, not by the (colourless and transparent) medium through which it travels. That is why light refracted by a prism changes direction (at the interface air/prism) but maintains its colour.

Slowing down a light pulse to the speed of a bicycle, using a Bose-Einstein Condensate (video).

Photons can also be identified by their wavelengths, using a diffraction grating.

Gert
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