The RS-A will work in snow, but they aren't a good performer in snow. Of that there is no question. This is well documented on multiple tire survey sites and in road testing performed on the tire.
I noted above that their overall score on rain was a 6.1 out of 10, based on survey result of over 1400 owners of the tire. In the snow that rating falls to 5.1, which is definitely worse than average for an all-season and is the worst performance characteristic of this tire. However it is better than some of the other "all-season" stock tires on new cars.
My last Toyota came with Firestone FR-680's as stock. They are truly terrible. Much worse than the RS-A. And back in the mid-90's, I bought a new Caravan that came with Goodyear Invicta GL's, another truly terrible tire.
Good tires cost too much to install as standard equipment except on upscale performance cars, where buyers expect good rubber.
As far as sub-$20K cars go, the RS-A is one of the better stock tires you will find. I definitely would not buy it as a replacement, and if you ever used a good tire on a Mz3 and switched back, I expect you'd immediately notice the difference.
Since Goodyear does sell these tires for a hefty price, there is a chance that you could sell them as new off the car, or maybe even work out a trade-in credit at a local tire dealer who sells Goodyear, if you want to upgrade right away.
A new set of RS-A's in 205/50-17 will cost you close to $600. So Mazda should be credited as having tried to equip the car with a much better tire than what is normally found in this price class.