We have had some little black pebbles come out of the bath tub faucet. Yesterday there were a lot of pebbles coming out of the outside hose. Now there is no cold water pressure. Any ideas?

City water or Well?
On a well you could have picked up some sand in your intake line.

If you have old steel plumbing(galvanized iron) some times the rust in the pipe can break off and comes out looking like little black pebbles.
Take all your screens of the taps and run lots of cold water to try and flush out the system.
Do you have pressure anywhere in the system? It sounds from your post that you still have hot water which means that the main line coming into the house is OK