It would be better for you to buy extra 4 winter tire with rim. You original tire should be still ok for summer but since the original tire is so call touring tire, they have good performance in summer but wear out faster than all season tires. They may not be enough for winter after they are worn.
If you order the orignial tire from dealer it would be expensive, For the same money you could order four winter tires with rims from costco. Try rim size one inch smaller than the orignial tire. ( costco would know how to do it) .