**Is is possible? Yes.** 

Technology-wise, you would do the same thing you'd do for language localisation (see this [related SE question][1] for the specificities).

> Localization refers to the adaptation of a product, application or
> document content to meet the **language, cultural and other requirements**
> of a specific target market (a locale). [Source][2]

Seems like the definition fits the icon situation perfectly. **W3C** actually mentions "Symbols, icons and colors" in their list of customisable elements. Just as it happens with content, images are loaded with cultural baggage.

The **apple developers** site has some guidelines in respect to *internationalisation* too: 

> Create or modify language-specific versions of nib files, text, **icons
> and graphics** (especially those containing culture-specific images),
> audio, and video for each locale. [Source][3]

Now, in regards to the cases, that's a tricky one because it's not easy to hunt down some good examples, but take a look at this:

In **Bangladesh, Iran, and Thailand** the "**thumbs up**" gesture (facebook's "Like") is traditionally an obscene gesture, equivalent to the use of the middle finger in the Western world. Apparently nothing happened, but I bet it was something FB's developers and designers had to consider. 

Also, the [example from UX.SE][4] cited in the comments has a nice answer (too bad the Q was closed). 

> Animal symbols can also be dangerous. For example, owls symbolize
> wisdom in the United States, and an e-learning website may use an icon
> of an **owl** to symbolize that a user or student is performing well in an
> online course. However, owls symbolize stupidity in some parts of
> Asia, and Asian students may be insulted, not encouraged, by such an
> icon.
> 
> Religious symbols can, of course, be particularly sensitive.
> Microsoft’s geopolitical product strategy team once avoided
> embarrassment by preventing the release of the company’s Office XP
> software containing **a moon and stars astrology icon** that resembled the
> Islamic Hila symbol. When religious symbols cannot be avoided, they
> must be localized, such as when the Red Cross has been adapted as the
> Red Crescent in the Middle East. [Source][4]

One thing is sure: This is a job you can't do based on **assumptions**. Feedback or research is crucial.  

I found this interesting discussion in meta:

 - [Less confusing icons for localized Stack Overflow sites][5]

And some nice related articles:

 - [The Localisation of Visual Content, Images and Icons][6]

 - [Harnessing the Power of Icon Standards][7]

 - [Website localisation: three examples of best practice][8]


  [1]: http://stackoverflow.com/questions/4179000/best-way-to-detect-country-location-of-visitor
  [2]: http://www.w3.org/International/questions/qa-i18n
  [3]: https://developer.apple.com/internationalization/
  [4]: https://ux.stackexchange.com/questions/39641/are-there-any-commonly-used-icons-that-dont-internationalize-well
  [5]: https://meta.stackexchange.com/questions/252622/less-confusing-icons-for-localized-stack-overflow-sites
  [6]: http://www.business2community.com/content-marketing/localisation-visual-content-images-icons-0649437#M448rcYjwV1h0ZwH.97
  [7]: http://webdesign.tutsplus.com/articles/harnessing-the-power-of-icon-standards--webdesign-8431
  [8]: https://econsultancy.com/blog/64260-website-localisation-three-examples-of-best-practice/