I might be wrong, but according to what I have read, a horse can supply its vaunted 1 HP of sustained power through something like a working day. I'm sure that would be at their slowest speed though, walking, not trotting or galloping. So yes, your proposed need for a "transmission" seems correct. A treadwheel could theoretically be constructed then to convert horse linear movement to rotary motion, and then geared appropriatedly to power wheels, pulling a trailer all day. Of course you would need 400 horses in the treadwheel or multiple treadwheels somehow working in unison, with the horses wallking all day. The mechanical complexity would be enormous, not to mention (as above) the logistics of caring for the horses daily!
Beasts of burden were once used to operate machinery such as in grain mills, converting their linear motion to rotary motion, pulling lever arms connected to drive shafts while moving in circles. I think this was first done by the Romans, or at least they did do this if my dim memory of history is right. Another, possibly more modern and practical scenario, might be to use horse teams to drive rotary motion that would drive electric generators, which would in turn charge electric vehicles. This assumes electric tractor cabs actually exist, or will soon. If what the media reports is correct they should. Such a scheme would actually be "green" and renewable if the horses had a nearby pasture to graze and a source of water like a pond or stream to drink.
Of course, apropos to POA, one could, in theory, also use horsepower to charge the batteries of electric planes. Somehow I can't see this happening any time soon!