San'layn were all blood elves at one point which means they inherently look like Thalassian elves for the most part. However, their skin has become ashen in its pallor. Many are incredibly pale, but those who possessed darker skin in life, tend to have a range of darker tones beyond just white. Given they were once sin'dorei, their hair, facial features, and traits can be amongst any of their original peoples. However, their eyes tend to be a bit more stringent. Red is the most common color, but white, yellow, green, blue, or black (sclera and iris included) also do exist.
From there, it depends on rank. Clawed fingers/nails are quite common amongst any vampyr, especially the higher ranks.
Bat-like ears tend to develop beyond the bottom echelons, beginning amongst the Barons and higher. Some even have bat-like noses and teeth that are all sharpened to points.
All san'layn have long, sharpened incisors. While elves in Warcraft tend to have long fangs due to their lineages the shape and function of those the san'layn possess are different. Rather than functioning similar to predator fangs, which are sharpest at the tip, vampyr fangs are razor sharp all around.
The longest and most notable of these teeth are the canines, however between the lateral incisors and canines an additional tooth grows in that is also pointed and sharp. The canines on the jaw are also long and pointed. In total, san'layn have at least 4 long and wickedly pointed fangs. Some possess more. Some possess only sharp teeth. Teeth are not indicative of ranking, but some like to claim that the vampyrs with the longest fangs are the most powerful (not true at all).
The sharpness of any of these fangs is to allow for ease when feeding and to tear flesh from bone. A san'layn's teeth and jaw are as deadly as any weapon. Romantic partners should be wary when kissing, for it is very easy to accidentally cut yourself on your san'layn's fangs even without touching the pointed tip.
If a san'layn possesses wings, they are like that of a bat's, leathery and boned, without feathers. Some can shape-shift at will to hide them if they are powerful enough.
Physique tends to be lean and muscular, but this is not a change that occurred after they died. This is usually the physique due to the nature of who was on the field that perished and due to elven vanity. Many of the elves who died were in good physical shape, but there is variance amongst them. Undeath did not change what body type they had in life. Nor is it indicative of their physical strength. All san'layn have supernatural strength and speed, regardless of body type.
In regard to functionality of organs: just as Blizzard as confirmed if the organs of a Forsaken are intact, they work, so do those of a san'layn. Whether or not you desire to have their heart beating if a personal choice. A beating heart would increase blood flow and metabolism, which means they would likely need to eat more, but might also be stronger than those who do not have a beating heart.
That being said, they are undead. Without some kind of magical work around, they are not capable of having children. At least, not the women. Men… that's up to the writer whoever you'd like to work that out or explain it.
Whether or not your san'layn feels cold, hard, and undead, once again, is a personal choice. They could be warm due to magic or the fact that their heart is beating or an illusion they use to lure people in. Remember, as long as it can be explained in a logical way, why not?