It depends how far past the apocalypse are you?
Tyres have a finite life. On rough or even slightly rough terrain larger wheels are better than small ones by a huge margin. Caravans are really only suitable on roads. Also you get caravans with 2 wheels and others with four. Most I have seen have just 2. The difference between your horses carrying some of the caravans weight as compared to it bearing it's own weight would be huge even on modest inclines.
All in all a caravan is suboptimal compared to a cart specifically made for it. Modified by extending the axles to allow for large wheels is your best option in which case there would be no difference in horsepower needed than a cart.
A carriage would be superior in all other ways. A caravans suspension, weight distribution and everything else are designed for good roads. If you've ever hit an unexpected bump or pothole with a caravan even at low speed you'll understand. Bottoming out with your unmodified low caravan would be a constant hazard.
It's a good idea though if you modify the caravan to suit. My suggestion would be to remove all the suspension and running gear and replace it with that from the back of a light truck with high clearance. The suspension then would be much more suitable since it's designed for a higher weight and the high clearance and bigger tyres would make even more difference. Not as good as a carriage suspension wise, but a solid practical solution. No specialised engineering needed for the modification. The hardest bit would be designing and fabricating the harnesses, which you have to do anyway.
Assuming your engineer has a bit of imagination you can run a generator off the differential or a wheel trickle feeding a battery bank and have all the comforts of home and lighting for night travel, spotlights for hunting or defence purposes etc. Link a trailer to the back of the caravan and you take the weight off the horses (the trailer will pull the back of the caravan down like a counterbalance), have storage room for a battery bank and other things and would probably just need an extra horse if you load it heavily. It would be much more stable like that, essentially you'd have 4 wheels with a pivot point in the middle. Your engineer would tweak all these things to work best for your situation.
I would think you could get 3 mph out of two horses on level good terrain with ease with the setup I described. Which is pretty much perfect since it's around the same for a human. Have another couple of horses for gradients and things or replacements and you should be good to go travelling. Steep gradients and rough terrain could be passed by separating the caravan and trailer and moving them separately and adding your riding horses.