Okay, jaq, by now you've seen enough responses to know that there's no consensus! Here's the deal:
Coaches and programs differ at the DIII level. There are some *highly* competitive DIII programs that would have zero problem with your doing two sports, particularly if (as you seem to suggest) the two are complementary. The beauty is that you could actually have *two* coaches going to bat for you with admissions!
There are other DIII programs wherein the coach simply can't be bothered with someone who won't make a three-season commitment to running. Some of these programs are also highly competitive, but not (by any means!) all. Most of them would be lucky to have you; but they may also have a philosophy of training, team development, etc., that would make them willing to give up a *solidly* talented DIII runner like yourself.
The key is for you to call the coaches (both the xc coach and the "other" coach) at each of the schools that you might have some interest in, and find out their policy. Schools and coaches just vary so much, and sometimes quite unpredictably (that is, a coach may have a rep as a "hardnose" and yet have no problem with dual sports).
My personal philosophy was that I wanted people to be three-season *athletes*, but not necessarily three-season runners. (Sorry for people in the Commonwealth--I know "athlete" pretty much means only "runner" for you. In the US, it denotes any sportsman.) I had a cross-country MVP who did x-c in the fall, swim in the winter, tennis in the spring, and triathlon in the summer. Fine with me. Without his being able to do that mix of sports, we wouldn't have had him at all, and the other guys on the team would have been worse off for it.