First of all, as you're mentioned the reason to change that are cookies - there's no need - see "sub-domain cookies, sent in a parent domain request" on Stackoverflow:
The leading dot in the domain value .example.com means example.com and its sub-domains. Without the leading dot, the cookie is only valid for this specific domain.
Note that when setting a cookie, domain values without a leading dot will be prepended with a dot. Only when the domain parameter is not set the user agent assumes the current domain for that cookie.
SEO-wise: If you go with "www." or without is not important, as long as you 301-redirect from the one to the intended one and all webmaster tools know what your intended domain is. BUT: If you would change this in an existing project, keep in mind the already existing backlinks and if it's worth to redirect them and possibly lose some link juice.
