Is it the cooking station you purchase with writ vouchers? Because if it is just a fire pit that you created with a regular plan, then I don't think it's designed for cooking.
If you mean the provisioning station in housing, yes it does work, but you have to position it so it isn't clipping anything else. This can be especially difficult on uneven ground. The outline should turn green when it's in a good position.
Tip I learnt on the PTS. If you want to put it on uneven ground. Buy the long oblong stone, and position the stone so it is stood upright, with just the very tip above ground. You can then place the cooking station on top of the stone, and it looks like it is on the ground, but will now work.
ETA - This is for the provisioning station. Anything else called cooking pot or oven, etc. doesn't let you cook on it, it's just cosmetic.