Totally depends on the year, how much, above where and the quality of it . However, you should figure on there being snow from the area of the fixed ropes onward. Most of the snow will be mixed rock, ice and snow. Don't wait too long to put on your crampons - there are not many good places to stop and put them on in the fixed ropes or afterwards. Look at the pictures posted on the Matterhorn page to get an idea of conditions encountered.