Hiking
There are lots of hiking trails in the area around Mase. If you're coming in the winter, a hike with snow shoes is definitely a great outdoor activity if you're not skiing.
The 'Bisse Tsa Crêta' is a path following a small stream, called a 'bisse' in Switzerland. The start of the hike is just a few steps away!
https://www.les-bisses-du-valais.ch/fr/Bisse/Bisse-de-Tsa-Creta/#situation
You can also hike up to a place called 'Le Rimble' and enjoy the views from this mountain pasture.
The Nax region tourist website offers more information about hikes around Mase: