I'm not an expert on tire fitment widths. However, 245s are comfortably doable with a suspension drop and a light fender roll. 245 StarSpecs will about hold fully-bolted MS3 power levels, around 320-350whp depending.
My 225 RE050A tires hold lightly-modded power levels just fine on reasonably pavement, even holds 2nd gear in the rain pretty damn well. Stock Gen1 is 215 wide, stock Gen2 is 225 wide.
Regarding winter tires, you're buying into the AWD myth hook, line, and sinker. AWD will only help with acceleration, it will NOT help with braking or turning, the two important aspects of winter driving. I will only advocate dedicated summer/winter sets unless you live in a place that only sees a few days below freezing every year. With real winter tires I bet I would out-brake and out-turn anything with all-season tires in the cold/ice/snow. In the summer I'll do the same thing with my real summer tires, dry pavement or rain. I like having that performance on-tap. I've never been stuck in any NH winter, nor gone off the road, even with my rwd Crown Victoria.
As for the costs, I put together a complete winter set with wheels, TPMSs, and tires for about $500 from CL and Mazda forums. I down-sized to 16in winter wheels which has many advantages: a wider selection of much cheaper tires (3 tires/$200 ea for 18in, 9 tire/$100-140 ea for 16in), softer ride over frost heaves, and no snow build-up inside the wheels because the brake calipers sweep them clean. I also don't have to risk damaging my wheels and tires swapping everything back and forth twice a year at a cost of $80*2=$160. My winter setup has about paid for itself in tire changes in 3 years, and will nearly pay for itself again when I buy new tires. I'm also not one of the eleventy-zillion people lining up outside every tire shop the first day it snows.
My $0.02, wheel/tire setups are something that I've put a lot of thought into.