Dec 17, 2015 - 4:12 PM
Hi E, and welcome to MySwissAlps!
I suppose you mean the Swiss Half Fare Card, right? If so, you can purchase a 50% discounted ticket to Zermatt in Zurich. There is no need for reservations, and you won't be traveling on the Glacier Express. Theoretically you can, but it would be a waste of money to pay the reservation fee for such a short leg. You simply take a regular local train, which is the more flexible option as they run more frequently.
For your information: if you take the quickest trains to Zermatt you won't be touching Brig (see the timetable). You'll travel from Zurich to Visp, there you'll change for Zermatt. The trains to Visp allow reservations but very few people book these (you can purchase them on the 8th if you want to). The trains to Zermatt do not allow reservations.
Enjoy the ride!