Yep, it should certainly be big enough for a 14h to 15h horse. My main concern would be the various other parts of the trailer. Make sure the rust hasn't worked it's way through the metal, as that's going to affect the structural integrity of the trailer. Is it single axle / dual axle? Tires aren't dry rotted and going to come apart going down the road? You're able to jump up and down on the floor without it sounding like it's going to come apart? There's no sharp objects on the interior of the trailer which could injure your horse?
I'd get another opinion from a friend of yours locally such as a mechanic or someone else that's car saavy that can look the trailer over. If it's really in good condition, paying cash for a trailer is always a good thing.