Is there a separate shut off ahead of the tap and not requiring shutting down the whole house?
If there is, damage or the hose was not disconnected there could be damage, but that can be repaired easier when it is warmer.
Usually, a shut-off to and exterior tap has a valve ahead of it. If so, shut off the this and open the exterior tap and then go back to the line shut off and slightly open the "bleeder", usually a brass cap with a hole in it, to allow the water to drain our slowly outside as the lower part of the line thaws.
Then you can repair any damage if the initial plumbing was done properly. - This is an annual ritual I go through and put on a styrofoam "bootie" (about $2 at a big box or walmart to prevent any possibility of freezing. With a good freeze free outdoor tap, a "bootie" usually does a great job after the hose is disconnected.