The vitamins are still in there; actually even more than if you'd steamed them, because, as you noted, the water's all gone into the rice. Now, of course, some vitamins do deteriorate from heat, but on the other hand, carrots are a pretty tough, fibrous food, and it's easier for the body to extract nutrients from cooked foods, so probably the honors are close in the raw vs. cooked debate.

So, excellent way to sneak carrots into your girlies' diet! Only thing is, sheesh, don't use margarine (http://www.google.com/#sclient=psy&hl=en&q=margarine+hazards&aq=f&aqi=&aql=&oq=&gs_rfai=&pbx=1&fp=8e8f35a77978fbf6); that stuff is so bad for you that if you're going to cook with it, you might as well just go to McDonald's instead. Real butter, or real lard, or real coconut or olive oil, are all fine. Butter mixed half and half with coconut oil works exceptionally well as a cooking-butter substitute.