You will periodically run into a carrot at the top of a sub forum page. If you are the first to click on it, you get the carrot.
You will also run across carrot locators which will show you the location of the current carrot. Watch it, and when it says a forum title such as "horse stories and poems". Go there, and if you are the first to get there, you can catch the carrot.
There is a bandit who is quite sneaky and will appear at the top of your page every now and then and take a carrot from you. He'll even feed it to his horse right in front of you!
And as you have seen, you occasionally have the opportunity to steal carrots from an offline member. Whether you get one or not, well, I guess it depends on your skills ;) :).
TM Tardy's Chick "Hunter" - 13 yo Paint
Remmy - 18 yo Morgan/QH cross
Gunner 3/31/11, Heidi 7/2009 Miniature Sicilian donkey