The quick answer to your question is, "Yes, you can tow the horse trailer."
The long answer is contained in the above posts - the HD cooling is the biggest component that you definitely DON'T have on your KJ. However the other components are either on your KJ now or are easily added, with a supplemental ****** cooler suggested by LibertyTC being the most difficult addition.
It is a long thread but
this trailer hitch How-To is an excellent write-up. Kinda long if you read all the posts and it was written nearly 6 years ago but the KJ's didn't change much over the years.
I suggest that you purchase the factory 7-pin trailer harness, PN 82207248 and - unless your KJ came with the EVIC overhead console - you WILL NEED to purchase the supplemental harness PN 82207620. I stress that if you DO NOT have an EVIC overhead console installed from the factory you will need the supplemental harness as it powers the various connections provided by the 7-pin connection.
To use a brake controller for the trailer the factory harnesses include a brake controller wire which you will need to hard-wire into a brake controller. Your pickup most likely included a modular plug for a controller but - alas - the KJ uses the wire on the harness. Irritatingly, most KJ's - even without the trailer harness - have the brake controller wire in the electrical panel next to the brake pedal, but it doesn't do you any good until you install the supplemental harness. The bloody thing is just there - but the supplemental harness will make it easy for you to access and connect to the brake controller. The post linked above explains how to find it.
Next, depending on the year of your KJ, the ONLY thing it might be missing is the HD viscous fan, extended fan shroud and electric fan (a different electric fan than you have now.) I have looked every place I can think of to find the HD cooling kit that Mopar used to sell and I can't find one. Best bet is to try to find one in a salvage yard somewhere.
I say
might be missing as early KJ's included power steering coolers (a vertical cooler on the driver's side of the radiator) as well as transmission coolers which run across the bottom width of the radiator; you'll see the supply and return lines on the passenger side of the radiator. The factory ****** cooler is admittedly wimpy but most KJ's did have them. I believe that the HD cooling system was more to pull additional air across the ****** cooler vs the radiator so an aftermarket ****** cooler is in my future.
I would suggest a LoadRite hitch as you gain about 4 inches of length beyond the bumper which extends it far enough back that you will find it easier to connect your trailer without having to resort to a 13- or 16-inch ball mount.
My apologies for the length of this reply. I installed the factory hitch and factory 7-pin harness and supplemental harness over the winter and for me a plug-n-play installation makes life easier. (I used the factory hitch as I found a GREAT deal on a spotless factory hitch off an '07 KJ, though I'm paying for it by having to use an extended ball mount :disgust: )
All that I've described can be installed by your dealer - a local dealer here was happy to do it for $400 labor plus the cost of the parts. No thanks...:freak3:
Let us know what you end up doing!
Bob