It's really, really common for the center Cobra badges to get stolen. From the factory, 96s had one. So, unless you bought yours new...
They didn't come from the factory with a cobra in the front. Only the 2003 / 2004 came with a Cobra in the front grill stock. Everything else came with the massive chrome-plated plastic pony.
The one thing that differs from all the years is the rear bumper. I don't know what the 1993 Cobra had, but as far as all the rest:
1994-1995 saw "MUSTANG" embedded in the rear bumper. These years also featured "horizontal" tail lights, they would be switched to the "vertical" tail lights to better fit into the Mustang's heritage. (Look at Mustangs from 64 1/2 and on, they all had a recurring 3 vertical tail light design.
1996-1998 saw "COBRA" introduced to the rear bumper. The "nostril" hood was introduced. 1998 saw the return of Cobra R wheels, only with the lip modifed slightly. 1998 also lost the clock pod and changed fuel-system types. There are other minor details, but for the most part it's the same.
1999 introduced an all new system and Teksid blocks weren't in every Cobra. Many 1999 were recalled due to not making the advertised horsepower. 2001 was more or less the same as the 1999. In 1999 & 2001 (2000 was not made save for the R) they featured "MUSTANG" in the rear bumper again. The embedded "COBRA" in the rear would not return until the Terminator model introduced in 2003 and 2004.
Other notable differences off the top of my head from 99/01 and 03/04 include: Rear bumper, potentially changed front bumper, tail lights altered (orange left out), and the badge on the back went from SVT - Cobra to just the classic SVT. Much of this info does not include any changes to driveline or chassis, just
some of the basic cosmetic changes.
Literally, the cobra in the grill mod is so common that most people believe all Cobras come with it - stock. It's simply not true, it's just something that
everyone has done so almost every person out there thinks its stock.
Here's is a Ford stock photo in 1996 of an SVT Cobra showing the pony in the grill: