How is he being asked to lower his head? From how you've explained, it sounds as though his previous owner has been simply focussed on where his head is and not given a second thought to how the rest of his body is working.
If she has been getting him to drop his head, by 'see-sawing' on the reins or using gadgets, it's likely that he is sore and stressed because of this. You have to 'coax' ottbs not force them or they panic.
Sweating after 15mins of walk and a little trot - I would, as others have said, put this down to stress. TB's are naturally fit with good stamina. They build up fitness very quickly when in work compared to many other breeds, and hold their fitness for much longer when out of work than say, WB's.
Personally, I would much rather see a green horse travelling above the bit and a little hollow in the neck, but going forward, reacting immediately to the rider's aids and willing to go forward, than one that has it's head low but the body is doing nothing and has low reactivity.
Once you get a horse travelling easily forwards without running, reacting easily to your aids, understanding half halts etc. the head will come. The horse will be more willing to stretch into the bridle and lengthen and lower the neck. Forcing the head low, will tighten the base of the neck and lock the poll, causing stress and tension.