As long as you have decent, both quality and condition non-summer (e.g. all season, mud & snow) tires, you'll be fine with cables/chains. I believe most newer Mazdas come stock with all season Toyo Proxes. As suggested above, practice fitting your cables to your drive wheels (front), before your stuck on the side of a slushy highway. If your Mazda has tight clearance for traction devices, I recommend looking at SCC's "S" Class clearance cables, like the Super Z6.
Bring a small poly tarp, mechanics gloves, headlamp, and rags. Turn your wheels lock to lock for each side to ease installation.
What are the R-1, R-2 conditions that I hear about?
Although Caltrans does not post signs with these designations nor use them to announce chain controls to the public, they are used internally within Caltrans and the CHP as a kind of shorthand to describe chain restrictions and may be included in traffic reports disseminated by various news outlets.
There are three primary categories of chain restrictions, as shown below:
R-1: Chains are required on all vehicles except passenger vehicles and light-duty trucks under 6,000 pounds gross weight and equipped with snow tires on at least two drive wheels. Chains must be carried by vehicles using snow tires. All vehicles towing trailers must have chains on one drive axle. Trailers with brakes must have chains on at least one axle.
R-2: Chains are required on all vehicles except four-wheel-drive vehicles under 6,500 pounds gross weight and equipped with snow tires on all four wheels. Chains for one set of drive wheels must be carried by four wheel-drive vehicles using snow tires.
R-3: Chains are required on all vehicles without exception.
R-1 and R-2 are the most common conditions. A highway will often be closed before an R-3 condition is imposed. Some local areas may use variations of these designations. You must follow the directions on the signs posted for chain controls or any instructions given by Caltrans or CHP personnel at chain control check points, even if these are at variance with broadcast road condition reports or information contained herein.
What California Vehicle Code sections refer to chains?
Chain requirements are covered in the California Vehicle Code (CVC), Section 605 and
Sections 27450 to 27503.