Visibility can suddenly be poor and the clouds can envelop the entire mountain without warning. The Hakone Ropeway will still operate regardless but the pirate ships will be cancelled if it gets this bad.
The weather can be fickle and unpredictable so if in doubt, book a ryokan and stay overnight for a better chance of getting a good view. Visibility is better before 12pm. I took a 'before' and 'after' shot on the same cable car and you can plainly see how thick the mist is.