Is my dependent, age 4, considered a full time student if they attended preschool for more than half of the year?

No.

The term full-time student only applies to college students who have attended college for five or more months or part-months. 

There is no tax benefit to claim for your child, under 19,  being a full time student. 

Being a full time student simply allows the parents to claim a child, age 19-23, to be claimed under the "qualifying child" dependent rules.