Mitch is absolutely right. It's one thing if people don't wish to share their e-mail address, or they don't have one, but not to ask for it is a major breakdown.
Do you have a list of "things we want to have happen when a customer visits our tasting room?" You should, and getting an e-mail address (and permission to send e-mail to it) should be one of those things. Having a list like that ensures that your staff is aware of all the things that should be happening (and why).
But the foremost item on your list should be "Did our visitor leave with a positive impression of our winery?"