Long Slow Distance is a great way to start conditioning your horse. Start with just walking ( at a brisk walk) for a couple of hours, after a few rides and you see that the horse is handling the 7-10 mile trail rides, Add some trots in a couple of stretches of the ride. After a month or two, you can extend those trots to more of the ride.
Soft tissue, ( muscles, lungs, heats) do condition much faster than hard tissue( tendons, ligiments and bones) But long distance trotting is great for building bone mass and harding up the hard tissue.
If you get out several times a week and work at it, By summer you should be able to do an endurance race. Don't expect to win or be in the top 10, Ride your race and enjoy the experience, observe the vets and learn to care for the horse.
You may also want to look into a CTR, They are shorter distance, slower pace, but a good place to get your horses started in distance events.