If you were to put snow chains on your Crosstrek’s tires, you would seriously damage the wheel wells, undercarriage, fender, and potentially even the bumper itself, leading to thousands of dollars in damages.
In the event that you live in an area that requires snow chains by law, other types of traction devices—such as spring chains or AutoSocks—may be equipped, provided use of the device on your vehicle is recommended by the manufacturer. If you decide to use another traction device, make sure you take into account road conditions and tire size.
All in all, don’t use snow chains on your Subaru Crosstrek.