I have fairly harsh winters. I do not repot in fall. I repot in middle to late summer. BEFORE the autumnal equinox, after the summer solstice. In my climate the heat of summer breaks about the 3rd week of August. I usually begin summer repotting the second week of August and finish usually by first week of September. This works for my climate. This allows enough time for new roots to form and harden off for winter.
CAUTION - if you live in a hot summer climate, do not attempt summer repotting. I have fewer than 10 days per year over 90F (fewer than 10 days over 38 C ). I have what is considered a cool summer climate. Summer repotting in a hot long summer climate will be fatal. Summer repotting is a STOOPID move in Texas, Alabama, Louisiana, New Mexico, Arizona & California. Probably not good in Georgia, SC & Florida. At least in the southeast you have humidity.
I began summer repotting because personal life allowed very little free time in spring. I have since found that conifers in particular do well with middle to late summer repotting. I have found autumn repotting to be problematic. Fall repotting is okay if I am able to protect the tree from extreme cold over winter.
Spring repotting, works best for deciduous for me.