As already said, they have most mass near the rear, so the axles are closer to the rear.
The construction is also different. Cross members are lighter in a horse float and made from angle etc with a high strength manufactured timber floor bolted to it. The sides of the trailer also don't produce a lot of rigidity in comparison to a car trailer. Axles closer to the rear where the load and loading door are.
The car trailer typically has RHS main rails and cross members and has a truss type structure to pull a lot of rigidity into the chassis - this is more necessary due to the point loads from the car and loading stresses when the car goes onto the trailer. Axles are in a more regular position and are regular axles, not set low with stepped/drop axles like on a horse float.

