My two dogs love cooked carrots, but neither one will eat a raw carrot for some reason. Probably, if one of them would eat it, then the other one would eat it ,too.
Chipper is just a 6 lb Yorkiepoo; and he is old, so he might have more trouble chewing up a raw carrot; but Tootsie (part Queensland Heeler) can crunch down anything.
Maybe I am not making the carrots small enough, and if I grated them or even put them in the food processor for a few seconds, they would like it better.
Sweet potatoes are another favorite veggie that both of my dogs just love, and they also eat those when they are cooked.
When we have soup, which usually has all kinds of veggies, they happily eat their little bowls of soup, too. I think that most vegetables are just so full of vitamins and minerals that the more of them we can eat and feed our pets, the healthier we will all become.