Quick trawl around the Net suggests that the 1.6TD Mazda 3 has a maximum braked trailer capacity of 1 300kg.
So, to answer your question; if the trailer + horse + anything else you put in the trailer comes to 1 300 kg or less then you can tow it. If the total is more then the answer is no, you cannot use the .
In my opinion it is unlikely that the Mazda is going to be suitable.