While I neither agree nor disagree with Phil's assessment, I am going to play "Devil's Advocate" for purposes of this discussion. Anything further that I have to say in this topic will be from that point of view, and is in no means meant to say that I am right or wrong. I am not acting as the authority, here; I am, merely, presenting my opinions.
If we are going to read the rule, by the letter, then where do we draw the line between trooper and beast? According to the K-9's profile, they are not, in fact, troopers - they are beasts. Venusian Raptor - same.
ISC Iron Mastiffs are listed as Grunt Beasts, and are mortal, even though they A.I.: 3. Hinko Dragon Mounts are beasts, are from Mercury, have no Environmental Training, yet are clearly modeled with some type of protective masking on the heads (and, I believe I already mentioned, are from an extreme environment). Hunting Dragons are listed as Support Trooper and beasts. Does anyone think that Karnophages shouldn't be beasts? Rivet Bulls are beasts, and, being native to Dark Eden, have Survival Training. Equine mounts are, apparently, imported from a part of Dark Eden where there is no contamination, as they have no natural Survival Training, but are modeled with protective masks.
What I am trying to say is that the arguments may be made one way or another. In the absence of clarity and/or concensus, one should default to common sense. Failing that, players should agree upon rules beforehand. Otherwise, instead of having fun, we bog down into discussions of rules.
To me, I would not make beasts pay for environmental gear. Where would we draw that line? Must they, too, have night-vision gear if you want to give it to the handler/rider? I don't think so. I think that beasts being what they are are entitles to certain assumptions: they can see better at night, have not had their heartiness and natural instincts bred out of them by being "civilized" (hence their effectiveness in battle), and should not have to try to bite something or hear and or smell something through a filter mask.
They are animals, and are able to deal with environmental issues much better than mere martal humans.