When you share a Daily Horoscope in Facebook or Twitter, personal data such as date, time and place of birth are removed on the shared page. The same applies to personal horoscope data like additional transits or personal chart drawings.
The shared page does not enable access to data in your profile, e.g. stored birth data, etc. In order to see how others view the shared Daily Horoscope, you can log out of your My Astro profile and then click on the respective entry in FB or Twitter.
Here you can see an example of a shared page.