Is it ok to not use 'www' in my website subdomain url?

There is no real right or wrong answer to this question, it's purely down to personal preference.

The www prefix originated to specify web servers, for example you might have mail.example.com, vpn.example.com, san.example.com etc. www.example.com just became the standard for web sites, however it's not, and has never been required. As an interesting read, Heroku (Cloud Ruby Rails hosting) recommends using the www prefix (http://status.heroku.com/incident/156) but that's for reasons to do with DNS CNAME records, etc.

There is no hard or solid reason to, or to not, use the www prefix. Yes you could say not using it reduces your data transfers by a few bytes (HTTP Host header, cookies, absolute links) but you should always give both options. If you prefer no www. then set up a redirect to the main domain. The only consideration is canonical URLs (Google will see www.example.com and example.com as two separate sites, so it is generally good to redirect one to the other).

You could always direct enquirers to No-WWW.ORG, the organizers of which make the rather pithy point that one addresses mail to [email protected] not [email protected] so why should URLs have rôle domain name labels.

This is what the www. label is, of course: a rôle label. It isn't actually necessary to use rôle domain name labels for services such as mail, FTP, and the WWW. They are superfluous and ambiguous. (ftp.example.com. may or may not have WWW service, for example.)

A halfway house, that retains the rôle name, is to make http://example.com./ work like http://www.example.com./ and that is what most people do. (Note that the canonical way of doing this, as given, does not involve client-side HTTP redirects, and concerns about redirects are actually irrelevant.)

Of course, in an ideal world (as envisaged by Jim Nelson and many others), the WWW would have been brought kicking and screaming into the 21st century, instead of the WWW being the one shameful laggard, and such rôle names would be obsolete.