Snow tires work better in snow if they are narrow.

You won't believe how narrow snow tires are for rally cars - when they drive on snow, they pretty much ONLY drive on snow.

In Massachusetts, we do not often actually drive on snow, more often we drive on slushy, plowed roads, clean a couple of days later, and dry most of the time.

I use snow tires of normal width on summer wheels to get good wet performance.

The smallest I would go is 205 for the 2009 XC70. BUT, Your smaller tire should not rub unless the offset is less than the the summer wheels, which is what I suspect is the real problem.

Drop a steel wheel and measure from the back side of the rim up to the center opening. Do the same with the summer wheel. In reality, the measurements should be the same.

Your 215/55/16 should really be 215/60/16 to have the same diameter as the 225/55/16. That would have rubbed even more with the steel wheels.

As for the smaller tires fitting the rim width, that should not be a problem even if you went to 195/65/16.
--
Keeping it running is better than buying new