conditioning is definitely something to take seriously.
Begin with trot. You can do quite a bit of trot, much more than three minutes, if your horse is a performance horse. Work him on a lot of circles and serpentines to help him to warm up. This is important, and will help him to develope a strong topline.
IF you have the opputunity, work uphill. Its a great exercise for you and your horse, allowing you both to develope good balance and a strong back end. And we all know how important that is.
Work in canter for short bursts in varying speeds. Work slow circles, and when your horse has more stamina and strength, you know after a few work outs. You can do a a few bursts of higher speed canter really extending it. This will help him a lot
After you've done these things for a while your horse will really have developed a lot more stamina, suppleness, and strength..
For more specifics...it might help if you let us know what your horse is actually trained for....
pics may help too, to see which muscle groups he may need the most work on