i have a set of 16" x 6.5" mx-5 alloy rims that i used on my mazda3 as my winter set. i expect to use them now on my mazda5. the offset is 55mm compared with the mazda3/mazda5 stock offset of 52mm, which means the rims are 3mm more inbound than the stock rims, but i've never had any problems whatsoever with this setup.
i didn't go with 16s to decrease the cost of snows; i did it for (-1) sizing with a higher sidewall profile, which improves performance in snow by reducing the tire contact patch area. but your reason is valid as well: 17" snows tend to be a lot more expensive.
I just got Mazda OE 16" steelies with tire package (Toyo Observe G-02 Plus) from the dealer, at $916 OTD it was cheaper than anywhere else, might be cheaper in the US even since tires in Canada are expensive.