Fiasco Farm is usually said to have the most comprehensive good/bad plant list. http://fiascofarm.com/goats/poisonousplants.htm
It shows beets (top and root) on the edible list, though I'm not sure if "sugar beets" are different than regular beets?? Also... a few things on their list dont make sense to me (rhubarb leaves on both edible and poisonous list, same with lilac I think - just a few typos or duplicates that have never been cleaned up - but makes me leary to trust what I read). So... take it as you will. I've fed my goats beet tops, but they aren't very interested. I know people use beet pulp as a feed supplement... so I'd be surprised if fresh beets werent ok. But I'm fairly new, and definitely still learning.