An opponent controls a system with a hazard. He has his control node and a number of his ships in the system.
I fly in with my fleet to that system's adjacent sector. I initiate a space battle. I clear out all his ships. I get a free movement into the system.
Must all of my ships brave the hazard, before I can initiate an invasion action?
When you initiate the space battle: no as your ships have not yet moved in the system.
When you move your ship in the system as part of having won the battle (free impulse move): yes as you've entered the system.
Once you are in the system, you can initiate ground invasion: no.
If you retreat from the system or capture it and use it to generate ships if it happens to have a star base: no as hazard are only tested when you enter.