Rattle and clunk while towing

Sounds like its loaded "OFF" that is with more weight at the rear of the axles than the front.
Any trailer loaded like that will bang away as the towhitch tries to come off the ball due to no weight on it..

Time to check the loads I would say


Check your towbar bolts on the car. They could be loose as well.

If you have a Haymen Reece type hitch (square insert) then the clunking could be from the insert moving on the pin of the hitch.
That is why some have a small bolt on the angle to stop any movement.

I can sympathise with you, those rattles are annoying. I agree with all other suggestions as possibility's. You said you had tightened the slack adjuster on top of the tow coupling and it made some difference. This may sound stupid but I have to ask. Did you loosen the lock nut and wind the adjustment screw down into the coupling until it was tight against the tow ball, then back it off one half turn and tighten the lock nut whilst holding the screw in that position???
Also check you dont have a 2 inch tow ball and a 50 mm. coupling They are not compatible.
Have you tried using another tow ball to see if it makes any difference?? And have you checked the tow ball is tight on the tongue. some times if the ball is not tight the threaded shaft can flogg around in the hole if the hole is considerably larger than the threaded shaft of the ball.

If all this fails I would suggest connecting the float and tug, taking a measurement from the bottom edge of the coupling to the top side of the tongue. Then put a jack under the trailer coupling and lifting the trailer weight from the tow ball and then taking the measurement from the same points. if the difference is less than 2-3 mm the coupling is not likely to be the cause

I agree with most of the above
Horse floats normally do not have much of a Draw bar (mainly older ones & your sounds like an older one due to the hydraulic over ride brakes) & the dual axles are set in the center so their is not much down weight with or with out horses (ours was 12kg different) this was so the std station wagon would not drag its ass but makes them see/saw on the hitch the other problem is with the smaller & cheaper ones they do not have load sharing springs & often only have two sets of std slipper type now if it has this type it quite common to have the clunking (same noise as the Hitch) as the load is taken on the fwd axle the aft one can clunk and visa versa
I had this with mine it was a old small Karra Kar I changed the suspension to a load sharing still used the std slippers (hate them) but fitted the see-saw/load sharing to the centre & it towed better was quite & the horse loved it, as it got a better ride (lot less kicking, noise, etc you know when they are happy)
good luck