Tall 175/65 15 snows on a Miata?

I've had my first Miata (10AE) for over a year now and with some new summer tires it's even more fun than I expected. Since I had a beater with a heater last winter, I rarely drove it and I've logged very few miles this year since the commute is up to the attic (the Miata won't make it up the narrow stairs).

Wisconsin typically has several venues for ice racing, (Wisconsin Autosports Group, Fox Valley Sports Car Club, Central Wisconsin SCC, etc.) so I'm thinking of taking it to a few (weather permitting). My neighbor offered me a barely used set of 175/65-15 Blizzaks he had on a Prius he wrecked.  Will those fit on the stock 15" rims w/out rubbing?

Prius tires are very narrow. Should fit and generally be a little undersized for the Miata. 

In reply to petemc53555 :

They're only an inch taller than the 205/50/15s that half the world runs on Miatas. You'll be fine. Post a picture of them on the car. I was thinking of possibly "borrowing" my wife's 185/60/15 Michelin snows to use on my Miata.

Sounds about right.

We all worry about the diameter when radius is what is important.  

I seem to recall running 195/65R14 Blizzaks on my Wisconsin winter driven NA Miata without rubbing, which is about the same diameter and wider. The extra ground clearance was helpful and it actually looked pretty good on there too, filling in the arches a bit more than the 185/60R14 stockers.