This depends on a number of things.
I used to have an Apache Popup... that is how the spare tire was factory mounted on it, under the propane tank, in fact the same bolts that held the tank in place secured the tire... However a previous owner changed from the single tank factory standard to a double tank arrangment and thus changed the spare tire mounting.
My next trailer was a SCAMP, Lovely little polystyrene bubble bit more aerodynamic than your can of ham.
The spare here mounted on a bracket which attached to the BODY, not the bumper (though it did have a bumper) I do not know if your body is as strong as my hunk of plastic though.
My next rig did not come with a spare.. It came with instrucitons to call a professional tire man if you have a flat (What, they think I can't horse a 22.5" tire and rim... They don't know me very well do they)
(Well, to be honest.. .I'd rather have Goodyear do it, or Belle tire, or whomever the local expert is)
There are other ways to mount a spare too. There is a rather interesting mount designed for motor homes, but a "Stripped down" version of it would work with a trailer too (lighter tires) It mounts on your tow hitch and allows you to attach the trailer as well.
There are many options
(With the Apache I carried the spare either inside the trailer, removing it when parked, or inside the tow-car)