Your horse’s condition and fitness must be considered when contemplating any kind of exertional exercise.
Have they spent several months on holiday in a field and are just beginning to build up exercise or are they in regular work already and just need to ‘top up’ faster work in order to compete? It generally takes 8-12 weeks to achieve full fitness on an increasing exercise programme. This might start with 2-4 weeks walking under saddle or on a horsewalker before trotting and then cantering are introduced. Jumping is not usually begun before 6 weeks of work, including schooling on the flat, has been completed. Beyond this, fitness for hunting and cross country is best achieved via interval training 2-3 times a week, preferably up an incline of at least half a mile.
Factors compromising fitness will include soundness of the heart, lungs and larynx plus any predisposition to ‘tying up’, a metabolic disease similar to cramp in humans which some breeds of horse are genetically prone to. These can be investigated by a vet if you are unhappy with the way your fitness program is progressing – some have more serious consequences than others.