Difference between a 175 and 185 tire?

[NewbieChris]

tread width. wider is better for snow or any traction really.

[Shibby]

I was driving my wife's car today in the rain. There was a little incline coming from a stop on a side street and the tires kept spinning. She drives a 98 corrola. With snow coming soon I was a little worried. She has a 175 goodyear all season tire with good tread. Would changing them to a 185 all season make any significant difference?