I recently forgot to turn off proxy and connect through a premium account, will the owner of proxy server be able to use the cookies and access the account?
As mentionned by u2702, anything sent over HTTP via the proxy can be clearly read by the owner of the proxy.
In your particular case, since the login page (ONLY) was over HTTPS (and I suppose that by that, you mean that the other pages were over HTTP after the login), your password could not be compromised. However, any subsequent request on their site via HTTP would bear your session cookie with it. The proxy owner could easily impersonate you thanks to that cookie, as long as the session bound to that particular cookie is valid.
If you want to prevent future reuse of that session, you can simply logout from the website (via the proxy or not, does not matter), which will invalidate the session if the site is working properly. Ofcourse it could be "too late", if malicious manipulations have already been done via your compromised account.