Hey OP. I can hopefully help clear things up for you.
The weekly social stream sometimes has 343 hosting from the studios an playing some games with a guest, other times they host a community member on their channel. If the games being played are Halo 5 or MCC then you have a chance at getting the Ice Unicorn skin, the skins are manually granted by 343 after the stream. It can take up to a week for you to receive the skin as they need to go through all the played matches during the stream time frame.
When 343 hosts a weely stream they generally don't do it on an invite basis - you need to find and match with them in whatever playlist they are playing. Community members often invite players who are watching the stream. It doesn't matter if you aren't invited or aren't on the same team as 343 or the feature community member though - as long as you are in a match with them dureing the stream time (and fully complete that match) then you will be awarded the skin :)