In general, fall is the best season to plant shrubs (among most other types of plants, too). Of course, there are always exceptions to the rule, and many gardeners seem to count arborvitae among them. In fact, arborvitae is not different than most other shrubs in that yes, you can plant arborvitae in fall and it will likely establish itself more easily in that season.
The confusion probably arises from sights of arborvitae suffering from winter damage. Fall planting of arborvitae will not put it at higher risk of winter burn, unless you neglect to keep it watered well, right up until the ground freezes. Established plants also require regular watering in a dry fall to help them resist winter damage.
Should you spray arborvitae with an antidessicant?
Diagnosing and preventing winter damage of trees and shrubs
Image courtesy of Proven Winners