Are their palm trees in Galveston?

Yes, definitely. Houston is a subtropical climate (USDA zone 9) and has very mild winters that allow for more stereotypically warm weather vegetation. The Sabal Minor, the Sabal Texana and the Sabal Brazoria are all native to the area. Many other non native varieties of palm are frequently grown in the area such as Washingtonia robusta (Mexican Fan Palm) and Washingtonia filifera (California Fan Palm)