Going into my 5th winter. Never used any extra weight in the trunk. I sense little difference between a full gas tank and a near empty one and that's about 100 lbs.
I didn't buy the S2000 because it was a "roadster". I bought it because it's neat little Honda and like any other Honda, I fully intended to drive it through the snow and ice. It does this amazingly well.

 

I have found that extra weight does help when it snows over a couple inches. I put a bag of sand in the trunk when it snows and take it out once the roads clear. On flat roads you won't notice too much difference but going up even a slight incline it make a big difference.

The negative handling effects of an extra 50-60 lb do not come into play in real life senarios when you are driving like grandma.

I like the idea of putting weight into the spare tire!