I know of many trainers who travel to their clientele to give lessons and or school the horse.
Depending upon the arrangements made lessons can be weekly, bi-weekly, monthly or any combination.
I've seen trainers from all disciplines come to instead of owner & horse haul to them.
What you must accept and realize though is now the work and responsibility all lies on you to provide acceptable riding conditions of a ring, jumps if you jump, barrels, poles, obstacles...specific sized arena if you do dressage and proper footing along with safe barrier to ride within boundaries as needed.
If you are limited in any of those items needed, then your lessons may not be as productive as once was when all the do-dads were provided you not realize you used.
If you choose to haul in to a barn you are not boarding at you can also expect to pay a fee, a ring fee and trainers fee for using the facility and their equipment during lessons.
This is also customary, or at least it was when I managed barns and we had a huge indoor and much use in inclement/winter weather conditions. But yes, traveling instructors and trainers do exist...
In fact, a few I know have produced some of the top equestrians of today in the professional ranks when they were juniors...and they hauled horses in to facilities to train at in winter ,meeting the trainers at specified time and locations.
I also know national reining champions who teach students at barns besides theirs too...
You just pay for that luxury and accommodation.