Unfortunately, there really isn't any way to guarantee that things won't move now that they're in place and were apparently constructed without thinking about what winter conditions might do. That's the bad news.

What might be good news is that the walls appear to be small and don't appear to be individually retaining great quantites of earth. That seeming to be the case, movement of any kind may be so small as to be unnoticed. One can only hope at this point. Over time you may see some movement.

Good luck.

You need to relay the wall untop of a level base of about 2 or more feet of gravel on top of undisturbed subsoil and you need to course the stones level so they rise and fall in unison. It takes quite a bit of effort to get it right.
200 yrs back a man skilled enough to do this commanded the wages of half a dozen laborers.

I would just wait and see what the first Iowa winter does to them. Relaying sounds like a lot of work. They are very pretty!

i know one thing. the next time i undertake anything with stone, you guys are going to get BOMBARDED with questions on what to do and what not to do. as i'm pretty sure, this winter they're going to slide right down the incline.

There are a couple of things that you can do next time to insure that the walls will be more stable through the winter. Always make sure that your seams between stones do not line up. I noticed there were quite a few spots in your picture where the seams line up vertically through the rows of stacked stone. Also, every 4 or five feet of the bottom layer of stone, place an anchor stone in the row. That would be a long stone, placed perpendicular to the row, to help anchor the wall into the hillside.

Wall stones are the ultimate in garden terrace retaining systems. I learned the procedure I have used for a number of years from Old World stone masons in Iowa. Here are a few of the key elements:
Always run base course (keep level) at least 3 inches below grade, tipped back at a 7 degree angle.
Offset each successive layer of stone 1/2 to 1 inch, depending on thickness of the stones.
Additionally, a "dry wall" can be further protected from movement by lining behind the stone with typar (or some other pervious geotextile) and backfilling with a few inches of pea gravel.
It seems like most retaining walls are done without these considerations and it's just a matter of time till they start to come over.
Good luck.