Agree with others, that it sounds like you've been left in a difficult situation with a potentially dangerous horse. As others have said, as this is a lesson horse & likely deals with many beginners such as you that don't know how to get the best from him, he's had lots of practice at telling them... where to go!
I would firstly quit even trying to pick up his back feet as that's dangerous(& irresponsible of whoever's in charge to let you do all that without guidance
). I would also not attempt to punish a horse like this, be it poking him in the nose
or otherwise, considering he obviously perceives YOU as the 'rude' one who has no manners and sounds like an assertive type who may well just give you a stronger 'correction' for your insolence.
I think it's important that beginners are closely supervised around horses, because there is so much to learn & that can go wrong, even with a well mannered horse. What you need is a good, considerate instructor & if possible, an easier horse to learn with.