Your main concerns on the glacier is staying warm and staying dry. Even on warm days the glacier is (obviously) frozen, the air below it will be just a few degrees above zero (think of a fish resting on crushed ice in a supermarket). Because you're relatively warm, any contact with the glacier will cause it to melt (just a little), causing you to get wet.
This is complicated by the matter that you'll be working hard (possibly carrying rope and other equipment) at times, but also with rest periods in-between. Should the weather be very nice, you'll have the sun baking your back while you're freezing on the other side...
My advice is that you should wear undergarments that cover your entire bod (excluding hands and head. I prefer woollen ones, other go for more modern materials. Cotton is not very useful, as it get very cold once wet (from sweat or glacial water). A sweater or fleece jacket is fine, preferably one where you can regulate its heat (unbuttoning/unzipping the neck hole) if needed. Waterproof trousers is necessary unless you will be walking on an entirely flat glacier (no climbing). A jacket is less important than trousers, again depending on the climb involved - and the weather! Remember, it could be raining.
Exercising on the glacier can cause wear and tear on your garments. Do not bring your newest clothes!
Of course, you should get in touch with the company you plan to go with and check what their recommendations are. Some provide everything you need for free, others require you to bring most equipment yourself.
