Do people really care about higher moments? I have heard that people often handle uncertainty using point estimates not probability distributions. However, I have been unable to find any evidence for this in the heuristics and biases literature. I was wondering if anyone could point me to some relevant papers?

To clarify, there is no question whether some people have some beliefs about the higher moments of distributions. However, it would not shock to me to learn that when (for example) considering by how much the stock market will rise tomorrow, people form a point estimate (perhaps using historic averages) but do really not think about the uncertainty surrounding their estimate.
Perhaps there is some evidence toward your claim, but I would argue that in most situations, people do not use point estimates (although some "smoothing" likely occurs). In particular, there is no doubt that people care about the second movement (variance). The commonly employed, and robustly empirically documented, notion of risk aversion captures exactly this. Given two risky prospects with the same expectation (say different assets) it seems that most people prefer the one with lower variance (i.e., the less risky prospect). Think: which would you chose when given the option between \$50 for sure or a 50/50 toss up between \$0 and \$100? The difference between these two options is entirely in their second moment. 

The evidence for this is so vast and varied it is hard to even give an encompassing reference; but since you ask about the stock market, it is worth pointing out that one of the key explanations for why stocks have a higher average return than bonds is that they are more risky. I imagine a google scholar search of 'risk aversion in the stock market" will be fruitful. 

It is worth noting that there is also empirical evidence that people care about the third moment (skewness). This working paper by Yusufcan Masatlioglu, A Yesim Orhun, and Collin Raymond is an experiment in which subjects 


  reveal a strong preference for positive skew over negative skew; in other words for ruling out more uncertainty about the desired outcome (and tolerating uncertainty about the undesired outcome) compared to ruling out more uncertainty about the undesired outcome (and tolerating uncertainty about the desired outcome).


As for even higher moments, the jury is out, but I would imagine their importance diminishes rather quickly. The complexity of the distributions needed to generate differential higher moments increases and I would think heuristics would start to kick in.