It could, but it might also lead to something harmful for the deer at the same time. I'm not sure if the gene affecting the deer's eyesight is known, but it could be a pleiotropic gene (a gene that influences multiple traits at once).

If that's the case, and the other effect is negative and somehow spreads through the population, it could become a future issue for the deer. Think about humans—we lost the ability to produce our own vitamin C. Almost every other mammal can produce their own (except for hamsters). When this happened, it didn’t harm us right away, so it spread through the population. But over time, it led to issues that weren’t a problem before, like scurvy.

Same could happen to the deer.

Only in areas with tigers, and then it would only express itself enough if there were enough evolutionary pressure exclusively on that survival tactic.

As long as other causes of death happen to deer in tiger territories and as long as speed remains a good survival strategy, minor mutations that would only provide an advantage in extreme specific scenarios like a tiger stalking them wouldn't have a chance to be spread.

There's also a whole host of additional brain power that needs to be dedicated to more complex colour blending and processing, and that may add enough delay to offset any potential gain in recognizing a threat.

Presumably yes, but its still down to a roll of the dice whether a mutation like that happens in the first place, and whether the individuals who have that mutation live long enough to breed, and whether that mutation actually gets passed down, etc

Competitive advantage over their deer peers.

It's been far more important, evolution wise, to be agile and quick enough to avoid predators. Like a security camera can only tell you how someone was murdered.

And then soon we'd have green tigers.