How do I preserve GIF animation with the image field and image styles?
It is possible, there already is some discussion:


Pure PHP with imageMagick - https://stackoverflow.com/questions/718491/resize-animated-gif-file-without-destroying-animation
Drupal discussion - https://drupal.org/node/1115658
Issue for ImageMagick module with patch - https://drupal.org/node/1802534 - several users claim that it is working.