A fridge produces as much heat as cold. Well u can't produce cold really. U draw the heat from the medium (air in this case) ans sweat off that heat (in your case into the same air) so its not doable like this.

Outhouse sheds are never a good idea really as sucurity becomes a serious issue due to possible light leaks, sound and the traffic in and out with water and materials.

If you can make sure all of the above is not a problem you still have to worry about kids or what have you snooping around.

In your case you need a way to get an even temperature in there that stays between prox 20-30 degrees C (68-86F).
The shed will have to be insulated and totally light proof. Insulated both because of temperature and sound as you will have fans running as well. If it is lightproof you will have to activelly ventillate the area to always keep fresh air inside. You dont have a similar area in your home you can box in to become a growbox for your needs?
I normally always advice against setting up in outhouses. But you know your surroundings better than me.

Puffzter