The car Matthew was driving was out-of-period, I think. The time frame had to be about 1920-21, and the car whatever it was looked to be something around late 20s or 1930.
If you mean the US "Season 3 finale", where Matthew has a fatal crash, this is actually the UK 2012 Christmas Special which has been tacked on the end of Season 3 for US viewers. The time frame of the episode is September 1921, (one year after the actual UK Season 3 ending) and the car is a 1927 AC Six, but the model was made from 1921 to 1930 so its appearance is not implausible. Its appearance in any previous episode would be anachronistic though. Some UK car purists have noted that car has front wheel brakes which only became standard in 1927, but they may have been an optional extra before that.
It previously appeared in a 1990s series called "House of Eliott".
The AC Cars company produced 2 seater sports cars in the 1960's that were exported to the USA to Carroll Shelby's facility where American Ford V-8's were installed. They were marketed and sold as Shelby Cobras. These now sell for large sums.
Here it is pictured after breaking down during filming.