UV lights have a combination of UV and visible light (unless you got one from a science laboratory where it is likely the whole output is UV for short wavelength UV). I guess the visible component is for safety reasons so people can see that it is on. As UV wavelengths are adjacent to the blue/purple end of the visible spectrum, they are often that colour if they consist of the visible.
LEDs usually emit visible light so you can take your pick over what colour that may be. However, technically the colour depends on the bad-gap of the semi conductor material. If you make the bandgap large enough, there is no reason to believe why you cannot have a UV LED.