1. Precog Reflector provides foresight before attacks are made. What about Powers that have nothing to do with Attack. Can you see them? I think not. It was modeled in some part on the Precognition power from the Heroes website, which states:
Heroes wrote:Precognition: You may choose how to put Energy into Attack and Defense after other people have revealed their choices. You must still choose which powers you are using normally, however.
Does "their choices" imply choices about Attack and Defense, but not about other Powers that have nothing to do with attack and defense? I don't know if I can answer it because the language is ambiguous, but my sense is that's correct -- Precog doesn't let you see Powers that don't have to do directly with Attack or Defense in that round.
2. Even if you could see other Powers, if two people have Precog, how do we resolve it? Both of you could see the others' attacks and defense and Powers, and could both adjust yours accordingly, but then you'd both foresee that and adjust again and so on in an endless feedback loop. I don't think that could work.
3. Then there's the issue of sequencing. Unless stated otherwise, all attacks, defense, and powers resolve simultaneously. In the case of Hyperspeed Attack 2.0, it was crystal clear -- it took affect (resolved) before all other Powers and attacks, including Mimic. Therefore, Hyperspeed couldn't be Mimicked.
Precog Reflector isn't as crystal clear, but I think the same reasoning applies. The precognitive foresight occurs before everything else resolves; since Mimic is included in that "everything else", I have to conclude that it's not possible to Mimic any Precognitive Power.
Anyway. Long explanation of this ruling: No, you can't Mimic the Precognitive Reflector Power. Even if you could, it's not clear to me that you would "foresee" the Snow Goon Power being used in a way that would help you.