When I was a child (or teenagerish), we took a trip to Canada and walked on a glacier. More correctly, we took a giant glacier bus to (and onto) a glacier, then we got out and walked on said glacier. It looked something like this:
New Zealand has a lot of glaciers. I don't know how many...and most of them are only accessible by helicopter or four day hike. But if you don't mind driving (a whole lot of driving), Fox Glacier and Franz Josef Glacier are both easy to get to. Remarkably, there are no giant glacier buses in New Zealand. I say remarkably because this country seems to love highly specialized automotive machinery (and we have the Antarctic Research HQ). [Aside: this country also loves using farm equipment for less specialized automotive uses.
But I digress. After your long drive, you can walk to within a couple hundred metres of either glacier. If you want to want on the ice, it is required (or maybe not required, but there are several warnings that you will die) to go with a guided tour (around $100 a person for a half day). If you have a little more cash, you can take a helicopter that will land on the ice and let you walk around. And if you are insane, you can jump out of a plane from above either glacier.
This is Fox Glacier from near the sky diving pick up site:
This is about as close as you can get to Fox Glacier without paying for a guide:
It was dark and stormy when we visited Franz Josef Glacier: