It implies that the sleep is brief, unplanned, and possibly stolen from a busy schedule.
Here are some examples of how you might use it:
* "I'm exhausted. I'm just going to snatch a few winks before the meeting."
* "The baby wouldn't stop crying, so I managed to snatch a few winks between feedings."
* "After a long day at work, I was happy to snatch a few winks on the train ride home."