I put 15" 7-hole wheels on my S and have had no problems. The narrower tires seem to be better in snow and the taller aspect ratio smooths the ride somewhat.
If you keep rolling through the seasons, then there's no need to fuss with changing tires or wheels. It's those of us that watch snow and ice fall from the sky that need the extra safety and mobility.
If you're interested, check the threads on snow tires, largely written by Canadians, to see how much time and cash we invest to keep our MINIs moving (in the direction intended).
Hmm - let's see - what's all the fuss about? Could it be snow (or lack thereof) in England vs. snow/ice/sleet in large enough quantities in Pittsburgh, Pennsylvania, USA to make an SUV scared?
Seriously - I want to get the high performance tires on my MCS when I finally get to order it in another month, but the weather in Ohio, USA in the winter is such that with the HP tires, you'd end up in a ditch rather quickly. I am definitely going to get some steel wheels and decent bad weather tires for the bad weather months.
The 15" fit just fine. The problem is how much the rims will cost you. By the time you buy the alloy 5-Hole MINI rims, and a set of good tires, you can buy the 16" non-run-flat package for just a few bucks more. For a few bucks more than that, you can get the 16" run-flat winter tire package.
The 15" in general, and especially the 15" steel rims were not recommeded by my dealer. But they don't know as much about the car as we do:
1. The 15" rims won't clear the larger brakes/rotors of the S. The S does not have different brakes. It has the same brakes as the Cooper.
2. There won't be enough clearance between the brakes and the rim to allow for snow accumulation. Then why is a Cooper with all-season tires OK?
3. The 15" rims won't dissipate enough heat for the extra weight of the S on the brakes. Especially the steel rims. So the brakes will overheat, in winter? Come on.
4. They don't make run-flat 15" winter tires. Yeah, so? So, MINI Roadside assistance won't assist you if you have a flat, and no spare, and no DSST tires.
Anyways, most of the above reasons are crap. But ultimately, it would have taken a long time to order the 15" alloys (which I wanted) or steelies (uglier) and then I had difficulty tracking down the tires I wanted. The whole thing was way easier to just buy the package. I splurged for the DSST ones, because I like the idea that Lady Leadfoot is safe when driving by herself.
Chilli Red/White Cooper S, Sport Pack & Sunroof. Delivered June 12th, 2002!
Now with MCS Winter Tire Package.
I wish we did the winter tyre thing here instead of putting tons and tons of mud/salt all over the roads for months... when it snows here, no-one has a clue how to drive and wouldn't dream of snow tyres/chains...
Of course the 15" wheels will work! In fact, some people (e.g. me) will argue that MINI handles best on 15" rims.
I replaced my 17's with 15 inch 8 spoke mini wheels w/continental all seasons. I found a set of takeoffs on ebay with only 10 miles on them for $329. After shipping, I was out around $390 for the set delivered. No problems with the 15's fitting, and the ride is smoother for a few months too!
BTW, I found a nice pair of mounting "spindles" at Griot's Garage to hang my 17's up on the wall for the winter. Very handy!
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Will the Cooper 15" wheels fit alright on the S ?? 
Chilli Red/White Cooper S, Sport Pack & Sunroof. Delivered June 12th, 2002!
replaced a 2001 BRG/White Cooper 
