When you play a real snare drum, there is a very wide spectrum of it's sounds. First you can tighten the snares underneath the drum.. this greatly affects the sound. Then velocity, strength, and where you hit the drum, actually creates a vast amount of difference. Some drummers will leave a cloth or their wallet on the snare, for a certain sound, to shorten it's decay rate. In a virtual drum kit. This extremely large variation is drastically reduced. The snares themselves (the metal wires underneath) really don't have much decay change, only the volume of them.
The newer, more expensive virtual instrument drum kits use a number of 'round robin' samples to accomplish this, and give the sound the 'human element'. Since drum synths, and sample libraries, we have become much more accustomed to not a wide range of snare drum sounds. But the human ear is quite adept at discerning when the same sample is repeated over and over. What you come away is, depending on the realism you are going for, depends on the virtual drum kit you use.
Yes, you can program snare sounds, and create some interesting results. You can google snare drums, and find info which might inspire you, or aim you in a direct to create what you are looking to do