Are the questions part of the assignment's "Description field"? If so, then on the Assignment settings page, under "Availability" you can "Allow submissions from" a certain date and uncheck the box "Always show description." Done this way, students will see the assignment name on the course page, but they will not be able to see the description until submissions are allowed. This approach should generally work without changes to admin settings.
In addition, though, Moodle also has something called "restricted" or "conditional" access. This feature needs to be enabled at the site level under Site administration > Advanced features > Enable conditional access. When enabled, Assignments and other activities should have a section in their settings called "Restrict access". Restricted access will allow you to hide an activity (not only an assignment) completely until a specified time or to show it grayed out with notes about the restrictions.
Restricted access is nice because of the way it works across activities and resources. In the case of Assignments it just happens to overlap somewhat with the activity-specific Availability settings.