Check out http://www.parkers.co.uk/cars/specs/ for the model/engine spec of the car you have and check the kerb weight, braked towing capacity and torque. The bigger the number for all of these the better and for somethi that is not a 4x4, staying within 85% of the braked towing capacity is a good idea.
It also depends what you are towing. E.g. an Ifor Williams 510 could be 1200kg before you add the horse, whereas a cheval liberte single trailer can be as light as 550kg without horse- quite a difference!
Do you have any more info? Might help other more experienced people advise you better?
Edited to add I've just had a look, and even the most powerful petrol engine is only listing a 1400kg braked towing weight.
The diesel only 1300kg. I'm not sure it's really a good idea I'm afraid.
Your Avensis has a max towing weight of 1300kg. A new Ifor Williams single trailer weighs in at just under 800kg. I have a 16h2" horse, he's fairly lightweight & he weighs in at about 525kg. This totals up to your maximum towing weight of 1300kg or just over. This is without any tack, hay, water etc. You would be on the maximum or possibly over. In that event I would say no your Avensis is not really suitable.....sorry
I tow my ifor williams trailer with a 3 series BMW. The towing weight for my car is 1400kg, the trailer is 900kg and the horse about 500kg. It tows fine!
Ask him to look at a mondeo? We have the 2.0tdci 130bhp version which has a 1800kg braked towing capacity, but still gives us ~44mpg daily doing in and out of town to work.
They're a bit longer and heavier than other similar cars and ours is certainly nippy and has plenty torque. Not yet towed with it yet, got that excitement ahead of us tomorrow!