As Skidpan mentions, brakes could be the headache here, ideally the ultra sensible 205/55 x 16 tyre and wheel combo from other E46 BMWs.
The friendly make specific forum BMWland would be a good place to ask this question.
An alternative size for winter fitments might be mentioned in your handbook, and might even be listed on the tyre spec/pressure sticker that your car should have, if 16" are listed there you should be in business.
If you're buying new tyres anyway then i would definately agree going all season makes sense, might be worth delaying the purchase of these though until the winter (we haven't yet had) season is over and prices get back to normal.
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