Privacy and confidentiality are different things...
A Zip file, even encrypted, is still there, and onlookers may observe not only the archive presence, name and size, but also the individual names and sizes of files within the archive, because these are not encrypted.
Traditional Zip encryption is weak and can be broken within a few minutes, regardless of how strong the password is — a good example of why homemade ciphers are an abomination. Some Zip-aware software can do better (e.g. with AES), but this may limit interoperability. For instance, Windows's explorer cannot open Zip archives encrypted with something else than the weak traditional stream cipher.
The normal, pervasive defence system of most people is to be utterly boring, thus making it unlikely that any potential attacker would bother trying to unlock their secrets. Yet, if you believe that an hostile adversary may actually try to learn your data and has access to your files stored in your cloud service, then you might consider making an unencrypted Zip archive, then encrypting that archive as a whole with GnuPG. GnuPG, among its many options, can do password-based symmetric encryption (with the
-c command-line option) and does it reasonably well. The presence and size of the archive will still be known to eavesdroppers, as well as the archive file name, but archive contents, including individual file names and sizes, will be protected.