Examples of environmentally influenced gene-expression in humans?

I think your question is interesting, though the use of "expression" is misleading in context of your rabbit example.

Examples of environmentally influenced gene-expression in humans? ... That is, a phenotype which requires BOTH a certain genetic background and particular environmental influences in order to be expressed?

In the example you give, the color-changing phenotype is not due to changes in gene expression but rather a conformational change in a tyrosinase variant at low temperatures that leads to decoupling of an inhibitor from the enzyme. This is not to say that there aren't any changes in expression with changes in temperature -- only that the phenomenon you describe is ultimately a change in enzyme activity and not the induction of a specific allele. See Kidson and Fabian, 1981 [1] --

It is proposed that at the normal body temperature of 37 degree C, tyrosinase from Himalayan skin is strongly bound to an inhibitor. At lower body temperatures, the affinity of the enzyme for the inhibitor decreases, thus allowing the synthesis of melanin to increase. This change in affinity of the enzyme for the inhibitor could be regulated by temperature-induced conformational changes in either the enzyme or the inhibitor or both.

Note that this study was conducted in "Himalayan" mice, not rabbits, though the authors do reference an earlier rabbit study [2] --

These results are in support of Danneel's visual observations ('41) that "ferment" activity of Himalayan rabbit skin is absent at temperatures above 25 degree C.

the full text of which can be found, in German, on Google Books.

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Concerning a human example of allele-environment interactions, look no further! The same temperature-sensitive tyrosinase mutation has been reported in people with oculocutaneous albinism (OCA) [3], albeit with a slightly different phenotype. From the abstract:

In this paper, we report a new type of OCA that results from a tyrosinase allele producing a temperature-sensitive enzyme. The proband had white hair in the warmer areas (scalp and axilla) and progressively darker hair in the cooler areas (extremities) of her body. Melanocyte and melanosome architecture were normal. Quantitative hairbulb tyrosinase (dopa oxidase) assay demonstrated a loss of activity above 35-37 degrees C. Plasma pheomelanin and urine eumelanin intermediates were reduced and correlated with hair melanin content. This is the first temperature-sensitive tyrosinase mutation to be reported in humans and is analogous to the Siamese mutation in the cat and the Himalayan mutation in the mouse.

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References

1. Kidson SH, Fabian BC. The effect of temperature on tyrosinase activity in Himalayan mouse skin. J Exp Zool. 1981 Jan;215(1):91-7.
2. Frisch KV, Goldschmidt R, Ruhland W, Winterstein H. Ergebnisse der Biologie. Eighteenth Volume.
3. King RA, Townsend D, Oetting W, et al. Temperature-sensitive tyrosinase associated with peripheral pigmentation in oculocutaneous albinism. J Clin Invest. 1991;87(3):1046-1053.

The breadth of examples of environmental exposure directly influencing changes in gene expression in humans is astonishing, occurring at every developmental stage from conception to death.

As an example, consider the environmental exposure to a reasonably high dose of a gram negative bacteria with lipopolysaccharide. Immune cells recognize this very particular environmental exposure as a danger signal, triggering a signaling cascade that includes activation of nuclear factor kappa beta, or NFKB. A series of changes in gene expression begins, including transcription, translation, and release of interleukin-1 and TNF-alpha, which are responsible for a host of externally observable changes, not the least of which is an increase in your body temperature. You can read about this generally in any introductory clinical microbiology or immunology text. One example is Murray Medical Microbiology, Ch. 2.

In this example, exposure to an infectious agent is analogous to cold weather in the rabbit. Fever is analogous to the change in the rabbit's fur color.

As acvill’s answer indicates, the color change in rabbits is not mediated by gene expression. In the case of fever, though, it is, and may be a useful teaching example. Everyone has experience with fever and understands that fever is not the basal state, but a response to the environment. It is not hard to make the leap from that personal experience to the idea that the signaling molecules that cause fever are not typically present, but are in response to very particular environmental cues, and that change (from the absence of circulating IL-1 and TNF-alpha to the presence of IL-1 and TNF-alpha) is controlled by a famous and fun to say transcription factor, NF-kappa beta.