Greetings John:
Well, depending who you speak with, some suggest harvesting black walnut during low sap flow season - which is during dormancy, but not before spring leaf-out (which is when sap flow is at its peak). Conversely, other sawmills and loggers will harvest and mill black walnut year round regardless of high/low sap flow.
You certainly do not need to season the log before milling, as you can stack and dry the lumber after running the wood through the mill. Wood moisture content is something to consider after you mill the log, but that of course will depend on the end product.