I suggest you ask the trainer what they prefer. Lots of people start horses in the fall, then let them think about it and mature over the winter, and then start real work in the spring.
If you were sending the horse to me, though, I would get the horse fairly fit via groundwork before getting on this fall, and then would have to regain that fitness level in the spring before picking up where we left off. For that reason I'd rather have the horse for 2 months in the spring, and you would get a lot more training for your money than if the time was split between spring and fall.
So I think it depends on the trainer's philosophy and methods.