Walls over time can be destroyed by zombies, however if painted, at this current version, will be ignored by zombies who will concentrate on barricaded windows and doors to enter a building. While a slight oversight, you must be holding the planks and nails in your inventory to upgrade a wooden frame to a wall, and these construction parts can not be used if on the floor.
Right clicking on the wooden frame shows the upgrade menu.
To build a wooden wall, a player must first equip the hammer, build a wooden frame, and then upgrade this frame with further wood and nails.
To construct a Wooden Frame, a player would require for Level 1, 2 skill points in carpentry. For Level 2 it requires 4 carpentry skill, and the Level 3 wall requires 7 Carpentry skill.