So that is the classic beginner dilemma. Your tree will die outdoors but suffer indoors in winter.

Looking at the species natural distribution and the climate there I would cool it down myself and hope it shed its leafs and go dormant. Not many people have that option indoors.

The best recomendation for long term success in bonsai is allways to get more mature trees that are locally hardy and grow them outdoors. Bonsai is about creating an image of an old tree in miniature form. To be able to do that one needs healthy and strong trees. growing trees far away from it's hardiness zone is another challenge and can only be combined with bonsai for the most experienced growers. And even for them locally hardy trees are more successful.

I currently have my bonsais in potting soil. When should I put them in Bonsai soil?

When they start the bonsai Journey. From mature trees and forward. For most species that I approximately 5-10 years planted in the ground. 1-15 in a big pot and 20+ years in bonsai pot.

Obviously your final design will determine the time as well. Huge size bonsai takes much longer than small shohin trees.