I don't think you will notice any hit in performance. Log writes will likely be buffered and then flushed out to disk. So unless you have high disk load you will be fine. If you do have high disk load than you probably want more memory.
Nginx is programmed with an event driven methodology. This basically means that log writes shouldn't block the serving of pages. It's probably a separate process as well, so no interference or performance issues.
If you don't need the logs, and/or worry about the disk space they might take you can check the logrotate configuration for nginx (should be in /etc/logrotate.d, file nginx). The default is rotate for 52 weeks, meaning that logs older than a year are deleted.
