The Model T was available in either open or closed body. For practical use - cars driven by railroad workers, doctors, farmers and others who may spend more time on unpaved surfaces than paved have a greater chance of being in mud and grime, therefore a rubber mat appears to be more practical.
From an earlier post this list:
"1909-1910 --Off-white rubber in front; wool carpet in rear of touring. White rubber mat on rear of mother-in-law seat roadsters.
1911-1912 - Off-white rubber in front; cocoa mat in rear of touring.
1912-1916 - Black rubber front mat; cocoa mat in rear of touring.
1917-1922 - Black rubber front mat; wool mat in rear of touring.
1923-1927 - Black rubber front and rear of touring."
Would this indicate that all closed cars had rubber mats in the drivers area (front)? Not the cocoa or wool as some vendors offer.
The MTFCI judging guidelines show natural rubber (off white) through 1915, then natural rubber OR black for 1916, and black after that. I didn't find a separate listing about the rear mats, though they are mentioned along with the fronts in some years. I didn't find any details about various body styles.
Jim Finney has the largest collection of brass Model T closed cars and is perhaps the most knowledgeable person on their restoration. Jim owns a 1909 coupe, a 1912 town car, two 1914 town cars, and a 1916 town car. His cars all have rubber mats in the driver compartment. I've never heard or seen anything that would indicate that this is not correct.
Jim's 1914 town car:
Jim's 1916 town car: