FWIW, animated gifs appear to work with email in the new share sheets in iOS 6, which would automatically populate the gif in an email if the user selects mail:
NSString *gifPath = [[[NSBundle mainBundle] bundlePath] stringByAppendingPathComponent:@"volleyball.gif"];
NSData *gifData = [[NSData alloc] initWithContentsOfFile:gifPath];
NSArray *activityItems = [NSArray arrayWithObjects:@"Here is an awesome body for the email.",gifData,nil];
UIActivityViewController *activityController = [[UIActivityViewController alloc] initWithActivityItems:activityItems applicationActivities:nil];
activityController.completionHandler = ^(NSString *activityType, BOOL completed){
// item was shared!
// you can check if it was email (or another type, like facebook or twitter) in the *activityType.
// completed is YES if they actually shared it, if they canceled, completed will be NO.
};
[navigationController presentViewController:activityController animated:YES completion:nil];