Are there 'only gaited' horses?

I've been riding trotting horses for the past 20 years - mostly in the lower levels of dressage.

I am both broken (one hip replaced - one looking at it), and am moving to an area where there are lots and lots of trails.

Since a jarring ride is mucho uncomfortable, I was wondering if there are horses that prefer their gait over trot, and that don't have to be "trained" into gait all the time?