It goes back to the legislature, they are the one's who write the laws. Landowners have special privileges such as being able to hunt on their own land without a license,etc. I can only assume that the legislature followed the same thought process for deer hunting with no fee. They had to set some type of limitation on the amount of land, so they picked 10 acres. It falls in line with the 10 acre requirement for centerfire rifles.

Part of it may be to prevent someone who owns 10 one acre parcels, or 20 half half acre parcels or to the extreme, 40 quarter acre parcels from qualifying for free landowner permits.