Most 2WD rentals won't need chains or other traction devices. Tires stamped M+S tires with 3/16 of an inch of tread depth are allowed:
THE MOTOR VEHICLE IS EQUIPPED WITH THE FOLLOWING: TIRE CHAINS OR AN ALTERNATE TRACTION DEVICE; FOUR-WHEEL DRIVE WITH TIRES THAT HAVE A TREAD DEPTH OF AT LEAST THREE SIXTEENTHS OF AN INCH AND THAT ARE ADEQUATE FOR THE CONDITIONS; ALL-WHEEL DRIVE WITH TIRES THAT HAVE A TREAD DEPTH OF AT LEAST THREE SIXTEENTHS OF AN INCH AND THAT ARE ADEQUATE FOR THE CONDITIONS; OR TIRES THAT ARE IMPRINTED BY A MANUFACTURER WITH A MOUNTAIN-SNOWFLAKE, "M&S", "M+S", OR "M/S" SYMBOL OR THAT ARE ALL-WEATHER RATED BY THE MANUFACTURER AND THAT HAVE A TREAD DEPTH OF AT LEAST THREE SIXTEENTHS OF AN INCH.
Full bill text:
https://leg.colorado.gov/sites/default/files/documents/2019A/bills/2019a_1207_enr.pdf
It's a pretty low bar. All-season tires are generally stamped with M+S. The law doesn't require snow tires, just all-season tires that are not worn out.
It will prohibit the very worst vehicles, but will still allow vehicles not capable of the worst conditions.
How fast is your Mustang? I took a quick look at the Ford website and all but the Shelby's have all-season tires. Are your tires stamped with M+S?
M+S is kind of a joke. The other day I parked next to a Challenger. Not sure which one, but it was a faster version with tires that had no business in the mountains during the winter. They were stamped with M+S.