I don't know how the C is in the snow but if it's anything like my GIII or my 2010 Yaris HB forget it. If there's a snow storm stay home! I have the Blizzak WS70 and they work well. Discount tire can set you up with a wheels and tires. I put mine on when I hear the first snow storm is coming. Be safe, well worth the $$$! Maybe you have a 4WD for backup?
Do any of the C's come with 15" wheels? If so that wheel/tire combo would likely be compatible with yours. A higher profile 15" snow tire would likely be cheaper, and also better traction. Also, have a look at my posting here, these Corolla rims might work. A dealership service/parts department will be helpful: Second set of wheels for snow tires and TPMS Sensors | PriusChat