What are the main risks of a glacier in winter compared to the risks in summer? How can you deal with these additional risks? Which additional materials or thoughts do you need to have?
I would like to exclude all types of avalanches as an answer.
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I think you just excluded the main difference which are avalanches (on steeper sections). Another difference is the higher risk of freezing to death in winter but this is not glacier specific and even in the mid of summer extreme cold can happen at high altitude.
On a glacier there are three risks summer and winter:
The risk of slipping is more or less the same year round, especially when the glacier is frozen in the morning.
The risk of seracs is very hard to qualify. Generally seracs are moving a bit faster in summer but get brittle in the cold of winter. Best to stay out of a serac zone all year if possible.
The risk of falling into a crevasse depends a bit. In winter** many crevasses, especially smaller ones are filled with snow. Snow bridges are thicker as well. These factors reduce the risk of falling into a crevasse. However, snow may also conceal crevasses with a non load-bearing layer which increases the risk of falling into a crevasse.
Generally the risk of crevasse fall is considered lower in winter and skiing unroped is the norm while roped glacier crosses are the norm in summer. However, this is also factoring in the use of skis which distribute weight a lot better than snow shoes or just boots.
*Serac: a block or column of glacial ice, often formed by intersecting crevasses on a glacier. Commonly house-sized or larger, they are dangerous to mountaineers, since they may topple with little warning. (Source: Wikipedia)
**Winter conditions are not necessarily tied to the calendar months. In early winter there may be only little snow and it may be still unconsolidated. On the other hand, glacier winter can range well into May and early June.