Booking Manager has now for some time been integrated with Mailchimp that allowed you to send and manage newsletters directly from it.
Now with the latest update you are able to view the statistics for the newsletters that you already sent.
Go to Newsletters (1.) and click on Manage newsletters (2.)
Select the newsletter that you want to view (1.) the statistics for and click on Statistics (2.).
In Overall you will find number of statistic information regarding your newsletter (3.). These parameters are explained in more detail on https://mailchimp.com/help/about-email-campaign-reports/
In Details you see lists of e-mail addresses that have opened or not opened your newsletter or unsubscribed from your newsletter (4.).