The NPS has long had a web cam at Paradise so you can see what yo can or cant see,
However, as was frequently was the case, when Paradise was in clouds they only went ot 6000 to 7000 ft and it was clear above.
But how would you know this?
Well the Camp Muir cam is at 10,200 ft and looking down the Muir iceField, I personaly think if it not as a " snow field " because it has crevasses and all the bells and whistles, except movement, as a glacier.
Now you cen see where the tops aof the clouds are and head up the Skyline trail
A word of caution... the Muir is no cake walk, it is a serious snow/ ice climb subject to sudden weather changes... You need to be prepared for 00 visability and high mountain extremes... More than a few ill prepared hikers have died trying it.... but with proper equipment and safety gear, and a good knowledge of the mountains ....and humility... it can be as rewarding as a climb to the summit of the mountain.... maybe even more so.
An Ice axe and or treck poles are manditory any season and I suggest crampons for the descent late season... Bring a compass and pick up the climbers map of compass headings to use in poor visability..... and know hopw to use them...and a compass