Hi Doug:
Veneer trees are harvested every month of the year. However, the term "veneer season" generally refers to the non-sap running season or dormant season, beginning in Sept-Oct. and running through March depending upon your geographic location or latitude.
Timber sales w/ a high percentage of veneer trees will likely be harvested during the veneer season. Timber sales with a couple veneer trees can be harvested anytime of year.