I'm still having a hard time seeing how revealing the number of times an answer was nominated in round 2 would improve round 3. I'm guessing one of the ideas is to maybe encourage some people to provide some very, let's say unexpected, answers for round 2. Bonus if somehow a "very wrong" answer ends up somehow being quite popular for round 2, such that its surprise popularity may become a bit of a curveball for how people would answer for round 3, but I'm not sure how often something like that would really happen.
Another maybe interesting case is if the "actual answer" was something no one nominated in round 2, and so end up with the lowest nomination count of 1. Then you may have another case where if the nomination counts are shown, some people in round 3 could be torn between picking the actual answer vs a more nominated answer. Then again, maybe the drawing is just so off, that the actual answer would simply not realistically be picked by anyone in round 3.
Basically it seems like only if the number of times an answer was nominated in round 2 ends up serving more as misinformation, would then maybe make round 3 interesting to be able to see those round 2 nomination counts, and I'm just not sure that would happen all that much.
So I think I'm still leaning towards keeping things simple and not show how many times an answer was nominated in round 2. Though I'm not strongly opposed to doing the opposite, and maybe for the very first time this game is played, we could try that and see how it goes, and then reconsider for the next game.