What sizes of snow tires would work with my 15 Impreza Sport?

Hi. You have the sportier 50 series rubber on 17". Base model Imps have the SAME HEIGHT 205/55 16 setup, which is clearly more comfy on rough or snowy roads. So if you REALLY need snows I'd pick up some cheap alloy or steel 16" rims and mount the 205/55 16. It's your best option. You COULD go with ultra-knobby skinnier 195/60 16 tires for deep snow or ice, but you'd feel more handling compromise in normal driving on dry surfaces. The skinnier 195 will simply bite a BIT deeper in snow. But do NOT mount SHORTER HEIGHT tires, as you'll defeat your purpose. I also wouldn't go taller (like 205/60 16) because of possible clearance issues. (If you're unaware of scaling, just multiply the width of the tire (205 in this case) by the aspect ratio (50 or 55) to get the sidewall HEIGHT, then add it to the radius of the wheel (8 or 8.5" x 25.4mm/in) Hence 205x50+(25.4 x 8.5)=205x55+(25.4x8). The former handles more crisply, the latter more comfy, assuming the tires are the same characteristics and "personality". With snows always go cheaper (16 vs 17) and softer (55 vs 50) for comfort in the rough stuff.