I plan to visit Zermatt in mid April 2016 for 5 Days 4 Nights.
Arriving in the afternoon on the first day and leave to Zurich airport in the afternoon on the last day.
Appreciate some suggestion on the itinerary.
You didn't mention your interests but I think I can assume that you will want to hike around the area. Well, you have chosen wisely when you chose Zermatt! The choices are probably the most abundant, and diverse in the... world? The weather in April is changeable and it is in transition from late winter to early spring. Of course the must see is the Matterhorn and the chances of cloudy and overcast is high during these transition periods in the seasons. Depending on how much snow fell this winter some trails will not be accessible because of snow but the mountain cableways and railways should be in-service barring any closures for maintenance. Skiing may still be an option for you.
Visit the link below to get more information and come back to the forum if you have more questions.
Additionally these activity suggestions may be useful too: myswissalps.com/ zermatt/activities. If you have a wish list you can plan by the day based on the weather as explained by lkdf62.
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