My guinea-pigs have started going out to their Pig House at night. (It's a wooden playhouse with a wooden door and an inner screen door thats mesh on the top half, wooden on the bottom)
There's a bolt on the door that slides across and down. I could put a padlock on it.
My garden is pretty well fenced (between 4' and 6') The shed is half way down the garden (it's about 80' long)
It's unlikely anyone would break in TBH. The garage has got the usual gubbins in it, so is more of a target IYSWIM.
The main reason for not putting a padlock is in case of a fire- we've got a power cable and adaptor for light and heater in the pig house.I'd worry if I couldn't find the key quickly.(Though I could use a padlock with a number code).
When I was a child my dad always put a chain and padlock on our pig cage- the garden was easily accessable though.
What does everyone else do for their rabbits, chinchillas and pigs?
I'm a bit 
.