It seems 'honeymoon period' has worn off. Now, please don't start yelling out that the horse was drugged when you got him - I think far too many sellers are accused of drugging horses because the horse changes temperament after a few days.
The 'honeymoon period' usually lasts a few days where the horse is good as gold. In this time, they seem to be sussing the new owner out, and when they think they've got you sussed, the 'testing' behaviour begins. Some horses barely do anything other than trying to push a little into your space, but others will go all out guns blazing, and will turn into a bucking bronco when purchased as dead broke and quiet as a lamb.
The trick is, do not give him an inch. If he moves into your space, push him away. If he goes to bite, let him know that it's not on. Don't take any garbage from him at all. I know its a new horse and you want to kiss and cuddle and make friends and develop this 'mysterious bond' that you see on the Horse Whisperer, but this tends to be where new owners come unstuck and the horse turns into a lunatic.
As Tiny said, he's just measuring you up to see if you'll let him get away with anything, or if you're tough like his old owners. Usually once you get through this testing stage, then you'll be able to 'be friends'. I'm not sure if you've witnessed a new horse being introduced to a paddock of other horses that have already established their 'pecking order'... but its a good demonstration of exactly what I'm saying. The new horse comes in, they all sniff noses and squeal a bit, and then depending on how dominant the new horse is, they will start fighting - kicking, biting, invading each others space. This can go on for a few days, until a new pecking order is established, slotting the new horse into his place. Then they're all 'big happy family' and very little fighting occurs.