I would put it somewhere a little more accessible, since you need to plug the control into it and what not. A lot of people mount them under the hood, but that usually requires extending the cables. If you must have it in the bumper, I'll second Spencer's suggestion to put it on the other side of the divider you're holding it up to in that image. Then it would be behind the passenger side "wing" of the bumper, which is more exposed and easier for you to get to. Remember that your rad skid will eliminate your access to the area you're holding it up to.
Putting it on the outside of the bumper isn't a terrible idea - remember that a lot of jeep guys mount these on top of an exposed bumper and put the solenoid box right on top of the spool, exposed to all of the elements. That being said, it won't look pretty and the sun does kill stuff pretty bad around here, so the plastic would take a beating.