This depends on how much you trust your local network. Http isn't inherently dangerous, however the data leak could be. If you have a small network where you manage the machines and services it could be trusted, no problem.
If you could use ssl, you should, but if you can't like in your scenario, I wouldn't hesitate to use owncloud with http for local clients.
The other consideration is the sensitivity of the data on owncloud. If it's music, pictures, typical storage data, it would seem like less risk. If you're storing and transferring tax documents, trade secrets, nsa files, you should use https.
Keep in mind, https only encrypts the data while in transit, the files on your client and server are not encrypted while being stored unless you set that up seperately.