Yes, there are mutes for stringed instruments. There are many kinds:
violin mute - Google Image Search
Arco simply means bowed ... not sure why it's denoted since string scores usually assume arco. Unless the passage before it was marked in some other way (pizzicato or something). Perhaps it is just being very explicit.
With regard to what kind of mute to use, I think it's usually up to the player for the most part. But certain scores can certainly require a specific mute.