These horizontal lines are caused by the upward contraction of the forehead muscles, when someone is expressing a tense surprised emotion, or raising the eyebrows and upper eyelids during an alert state.
Some people worry that the Botulinum will make them look frozen. Normally this should not happen, and if it does even slightly, it is due to improper technique of the injector or too much dosage is being injected. Experience is important here. There is a chance of mild drooping of the upper eyelids for some older persons or if there is already pre-existing eyelids drooping.