Having not seen the episode, do some people get spaced?
If so, and assuming there isn't any other shenanigans, you don't need to worry about the cold. Space tends to be cold, but its also just barely even there. No air means no convection, and that means you'll only get cold very slowly. Much too slowly for it to matter in this situation.
Your biggest concerns are going to be preparation (don't hold your breath!) and getting back to an atmosphere as soon as possible.
The problem here is its kinda a meme. PIC S3 also did this, with Vadic, though she was a changeling.
I kinda wish there was a way to, say, use a mastodon account from another server on here.
Say, you could have a page on here, probably on the login page, where you can tell it "I want to use an account on another server", it redirects you to the other server which asks if you want to give permission, and you click yeah and then you're logged in on startrek.website using a mastodon account or whatever. Would be kinda cool, but it would need to be implemented properly and securely, which I am not capable of.