Have you had a look on ebay? If you do a search for 3.5 horsebox or 3.5t horsebox, that should return a variety of the smaller ones, then once you've had a read through the various types, you might get a feeling of what may suit you. I think the VW LT35 is fairly well regarded if you can't get a Master, or a Transit with a horsebox body on the back would be ok, but both of those will have quite a high unladen weight, and you'll have to corner slowly!
I have a VWLT35 and it has a payload of 1 tonne (1000 kg) - but you dont have to corner slowly (well, no slower than you usually would when transporting a horse of course!)
It is a fabulous little lorry, much envied by all on my yard, really easy to drive, well laid out, a brilliant first box
And no, I am no longer trying to sell mine, so this is not a sales pitch
Oh well that's good news, I was just going by what one of my friends said about hers, plus the fact they're up higher, but it could have been that hers had slightly soggy suspension!
Horses travel higher off the ground in a LT35 than they do in say a Renault Master. This means that, regardless of how carefully you drive, they will feel more "yaw" in the movement of the box round corners etc. It's about where the centre of gravity is. A lot of horses are fine with this, mine is. However, if your horse is a bit of a dodgy traveller think about it, because the horse will get a nicer ride if they are closer to the ground. Also the ramp won't be so steep, which helps a lot of unwiling loaders.