In the area around Muerren and especially on top of Piz Gloria / Schilthorn good shoes are a MUST !! Muerren is in a hight of more than 1200 meters and when-ever you take a hike, you never know what kind of surface you will have to step through : slippery, wet rocks or mud and high grass, cow-pats etc...
Never go without a good weather-gear - an umbrella is certainly NOT enough in the high mountains, where rain will mostly come with wind and storms !!
Miscellaneous: Some chocolate and an extra bottle of water makes always sense, because when hiking you never know how long you will have to wait for help in case of an emergency or when you are forced to get shelter in an empty mountain-hut because it is that foggy or raining outside that you cannot see, where you are going.
Bottles of the light PET-material are the best - you will not feel them, when they are empty, and you may fill them at many fountains on your way - the quality of the mountain-water is always excellent in Switzerland and the cheapest mineral water you may buy in a vending-machine is 2 sfr., mostly it is even more expensive.
Bring some old bread and other food for the birds, the swans and the fox on top of Schilthorn !! - see my other pics : that fox seems to live right under the platform of the restaurant. It carried food there and left shortly afterwards in order to find more food !
Remember warm clothes during winter. This winter is cold and very snowy. Skiing-clothes with warm underwear keep the cold at bay. Bring a good pair of boots with good, solid heels.
Photo Equipment: The cold can get the best of your camera, it's therefore a good idea to bring extra batteries and/or a charger.