Every trumpeter carried two instruments, the bugle and the trumpet. The instruments were used to play a variety of calls, and some were more complicated than others. So the trumpet would be used to play the more complex calls, the bugle was a smaller and simpler instrument and could be played on horseback. So when mounted for action, the trumpet would have it's cord wrapped around it and would be tied on the back of the trumpeter. Only the bugle would be used in action to play calls such as 'advance', 'charge' etc.
By the way, the 'charge' at Balaclava is generally believed to have been played by Trumpeter Billy Brittain, of the 17th Lancers, who was Cardigan's trumpeter on the day of the charge. He was severely wounded and died a few months later in Scutari Hospital.