Can an offer of free shipping increase sales to mobile users? (The words "free shipping" is not permitted by the California ABC, but "shipping included" is the same thing and this can be said.)
The answer is "it depends." Depends on what? Well, for starters, is your site optimized for mobile? If people can't order easily on your mobile site, it may not matter what you are offering. People will get frustrated and click off.
So the first thing you should do is make sure your site is easily accessed on mobile devices.
Then you should make it clear that you are offering free shipping. Buttons should be big and bold. People don't want to read the small print on a mobile device. It's too small.
If your site is optimized for mobile, then the answer is still "maybe." Shipping wine is expensive, and frequently a solution can be found by offering discounts and special deals, or even reduced price shipping.
What many wineries and other retailers don't realize is that they can have special offers available only to mobile users. Since mobile browsers can be identified by a site, an offer can be made to go only to mobile users.