A Google Webmaster Help thread asks if there is an SEO benefit to going the cookieless domain route.

The simple answer is that no, there is no direct SEO impact on going with the cookieless domain. But it can impact site speed, which is now a direct SEO factor, although it likely won’t have a serious impact if any on your rankings if you do use cookies, since most of the web pages on the internet that you visit and rank high in Google do have cookies.

Google’s John Mueller explains why people use cookieless domain:

But does it impact rankings? John said no:

For more on cookieless domains, see this page.

Forum discussion at Google Webmaster Help.