Mars does have a carbon cycle, and seasons, and the climate has changed over time. That’s a big focus of study by the Mars rovers. Here’s a recent article about Curiosity studying the climate of Mars. Curiosity and Perseverance also have weather stations. Here is the recent weather data from Curiosity, and here is the recent weather data from Perseverance.

The atmosphere is extremely thin, less than .01 Bars at dust level, and also extremely cold. No runaway greenhouse effect, quite the opposite in fact. The atmosphere has been blown off and almost all heat radiates away into space.

Global warming by itself wouldn’t be able to kill every living thing.

Most likely all life dies because it’s core cooled, which means it couldn’t be protected from radiation.

Much less dense atmosphere and further from the sun, so the effects would be less significant.