While Dave's suggestion of bracket (welded onto the side of the frame, not the bottom) is probably the best approach, horizontal holes through roughly the middle of the frame rail (not in roughly the top third or bottom third of the height) are harmless structurally. The key is to avoid corrosion, by deburring the holes and painting or otherwise rustproofing them.
I drilled 1/2" diameter holes like this through the frame of my trailer to mount shock absorbers; it was the standard installation method for the hardware kit I was using, and was not a problem.
BAL Retract-A-Spare Model 28240
installation instructions:
manual
Strangely, the end brackets have holes for both vertical bolts (which could go up into a floor or into the bottom face of the frame rail) and horizontal bolts (which would go through the side of the frame), but the instructions don't explicitly say which ones to use; the direction to use a bolt and nut imply that they are drilling right through and thus horizontally... and through an I-beam or C-channel frame since they are using a bolt only 1-1/4" long (you'll need much longer bolts. If just bolting, I would use horizontal bolts through the frame (as is apparently the plan here); if using welded-on brackets, I would use brackets which weld to the side of the frame and then vertical bolts through the carrier and those welded brackets.
One note: it isn't good to clamp the two side of the hollow frame rail together with a lot of bolt tension, but you need these bolts to stay tight. The use of self-locking nuts (they say "Nylon", but mean "Nylock", and any brand or type will work) is important.