We've done several glacier excursions over the years and always just worn water proof (or at least water resistant) hiking boots/shoes - something we normally pack anyway. But I've seen plenty of folks (especially kids) in just tennis shoes, though in that scenario I'd recommend throwing in an extra pair of socks in the backpack to change afterward. It's also been our experience if special cold weather gear is required beyond what they reasonably expect travelers to have with them, most tour operators will supply it or at least warn you ahead of time.