Until quite recently, snide meant 'fake' or 'false'. It appeared as a slang term in the mid-1800s, and was quickly taken into popular usage. The earliest written references are to "snyde witnesses" (1862) and "snide religions" (1868).
In the early 1930s it started to mean 'sneering', which has slowly morphed into the current meaning of stuck-up, rude, and perhaps sarcastic. Macmillan dictionary defines it as "deliberately unkind in an indirect way", variants of which are also used by the Oxford Dictionary and Merriam-Webster. WordNet gives a definition that perhaps better matches common usage, with the simple "expressive of contempt".