Mazda3 Snow Tires
 

Right now on my 3 I have 205-5-R17's Any reason I can't put on 195-65R15 steel rims with a dedicated snow tire?

Make sure that the inside of the rim clears the calipers... otherwise there shouldn't be an issue.

https://www.mazda3club.com/wheel-tires-67/fs-mazda-3-steel-wheels-tires-55228/
this poster is selling 15" steel rims - in case you're looking... so apparently they will fit.