From the text for Bridle of Tricks:
"While wearing the bridle, a creature is treated as knowing three, four, or five additional tricks, as if it had been taught the tricks with the Handle Animal skill. "
Handle Animal Skill:
"You can teach an animal a specific trick with one week of work and a successful Handle Animal check against the indicated DC. An animal with an Intelligence score of 1 can learn a maximum of three tricks, while an animal with an Intelligence score of 2 can learn a maximum of six tricks."
This is how you taught your mount the tricks in the first place, so with the Bridle your mount now has 9-11 tricks.
From the text on War Saddle:
"The saddle allows the creature wearing it to act as if it were combat trained (see Handle Animal for more information on combat training), and gives the rider a +5 competence bonus on Ride checks made while mounted upon the creature."
"Combat Training (DC 20) An animal trained to bear a rider into combat knows the tricks attack, come, defend, down, guard, and heel. ... The new general purpose and tricks completely replace the animal's previous purpose and any tricks it once knew. Many horses and riding dogs are trained in this way."
So combat training is a set of specific tricks.
If you already have some or all of those tricks, nothing happens to those specific tricks. While for any of the tricks listed under Combat Training that you didn't previously have, you have so long as the saddle is equipped. However if the animal was already trained for a purpose, it looses any of the tricks it gained from that training, but not any tricks you trained the animal in individually.
From the text on training an animal for a purpose:
"Rather than teaching an animal individual tricks, you can simply train it for a general purpose. ...
An animal can be trained for only one general purpose, though if the creature is capable of learning additional tricks (above and beyond those included in its general purpose), it may do so. Training an animal for a purpose requires fewer checks than teaching individual tricks does, but no less time."