It's hard to speak of what to do in MN but here's my thoughts in general. After that, you could consult a Home Inspector, perhaps a Municipal Inspector, or perhaps a Builder for more info.
WHen a crawlspace is directly 'connected' to a heated/cooled space, the space is left alone. If you were to cover it, then whatever moisture gets drawn to the surface will have no where to go once it gets to the surface. That is to say that while the crawl is UNCOVERED, the moisture rises up and out of the crawl, and has to go somewhere.
Now, I have to ask - if the crawl is vented to the outside (as you say), then why is it being heated? Do you mean there are heating vents 'connected' to the crawl? I'm not clear as to the relationship between the 2 'spaces'.
The white stuff may be phosphorous, or something. Have it tested if you want to know what it is. I don't think that you'll have to take any drastic measures, so talk around to get some answers. If you end up covering the crawl, you can lay pressure treated lumber along the perimeter. You shouldn't need to go UP the sides of the crawl. Just cover the floor (if directed to do so.)