A client's website is currently at www.domain.com, with domain.com redirected there automatically. I've suggested that they reverse the redirection to drop the "www", so I can set up a subdomain that can use shared session cookies (= login to domain.com stays logged in at sub.domain.com). However, they're concerned that the change will impact their search engine rankings. Any advice?
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:
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.