The only time I have lost control of my Boxster is in a blizzard, and of the two or three times it happened I was either driving to fast for the conditions, or shifting and the sudden change in RPM caused the rear wheels to slide out.
I would say 20MPH is too fast in a roundabout in heavy rain, and just about any car would have a problem at 20MPH in a roundabout in snow (I know the speed warning at the roundabout near me is 10MPH).
So while it could be your tires, I would experiment with different driving styles before I spent any money on new tires.
