I just took this tour. The group provided you with knee high rain boots with a slight grip on them. You can wear hiking boots if you want, but several parts of the trek require walking through water.
I didn’t find the boots offered great support, but I appreciated the knee high waterproof to keep me dry. I didn’t find that my feet were cold at all.
I don’t think I can give the tour company name out, but if you Google the name of the excursion, the company will come up and they outline all that they provide for your trip. They give you rain pants and jacket, rain boots, a dry pack, a filled water bottle to keep, a snack bag with lots of snacks, and a floatation vest.
For what it’s worth, the excursion was great, but they will not walk you directly onto the glacier because it is no longer safe. You do get very close to the glacier though and it was quite a fun, but strenuous, trek.
I can answer any other questions if you have them!