Are there any exotics that can be hunted at any time of the year?

Two of our most populare Texas Exotic species can be hunted anytime - these are Blackbuck Antelope and Axis Deer.  The Blackbuck Antelope never shed their horns so they are available year round and the Axis Deer shed their horns determined by their birth date and not a specific time of year.  When a ranch hosts large herds of Axis Deer as ours do, there are always some Deer in hard horn and a few in velvet.