Is it against the law to break someones nose if he is on your property?

Even if someone is on your property, you do not automatically have the right to physically assault them. You have the right to protect yourself and your property, but the force used has to be comparable to the force being used.

If they just walk onto your land, perhaps not even being aware of it, you cannot attack them. You can ask them to leave, you can call the police or ignore them.

If the individual has a Baseball bat and is going to break Windows are attack you, you have the right to protect yourself. If a reasonable person would be in fear for their safety, you can protect yourself.