Yes, updating through XenCenter is one of the features of the paid edition. On the free edition you need to (I somehow missed that difference between 6.2 and 6.5 - indeed Xencenter 6.5 allows updating 6.5 Xenservers via Xencenter even in the free edition)
Alternatively you can as always apply patches from the command line, the correct procedure is explained on the patch notification page (see here for an example). The shortened and generic version of what needs to be to install hotfixes done, copied from that page:
- Download the update file to a known location.
- Extract the xsupdate file from the zip.
- Upload the xsupdate file to the Pool Master. XenServer assigns the update file a UUID which this command prints. Note the UUID.
- Apply the hotfix to all hosts in the pool, specifying the UUID of the hotfix
- Verify that the update was applied by using the patch-list command. If the update is successful, the hosts field contains the UUIDs of the hosts to which this patch was successfully applied. This should be a complete list of all hosts in the pool.
- To verify in XenCenter that the update is applied correctly, select the Pool, and then click the General tab. This displays the Pool properties. In the Updates section, ensure that the update is listed as Fully Applied.
It looks like a lot of work but with some exercise it's not that much of a hassle :) and if you're working over a slow (WAN) link, it might even be more comfortable. For some patches (eg drivers) the procedure may be different, but the proper procedure will always be explained on the notification page.
I also recommend you to subscribe via this page to get alert mails every time a patch comes out.