Hehe, I just thought of an ingenious solution for making the outdoors mostly safe while using very few cheap materials. Camera balloons! With 4 people (6 is better for redundancy) you could have it operating continuously (until one of them got tired and had to sleep or got bored and stopped functioning normally. That's why we need to couple all humans with an AI that will keep them functioning properly at all times).
Assuming they're not on a time limit. I've been operating on the assumption that the effect is touch based or at least range based. Maybe some sort of personal dimensional or time field surrounding people, some sort of field of personal possibilities or maybe even dreams that when observed collapses into reality (which would explain any strangeness seen in them). And approaching said field causes certain brain patterns to be transferred to yours, triggering the field response on yourself. You know, space magic zombies. Probably triggered by an artefact meant for aliens that process the world differently. Probably the same artefact causing the dome. Just conjecture of course, I have nothing to back those statements up other than gut feeling, which is probably wrong.
FAKEEDIT: Unless it's turn based, which makes the above unnecessary.
Of course, nothing beats a defence against blink monsters like forming a testudo. Except maybe throwing or demolishing stuff, if those things can throw things or are smart enough to damage the environment and thus attack you indirectly or blind you long enough to attack you directly. You could check the environment for damage on the barricades. Although, judging by the size of the barricades, I'm going to assume that they can damage them.
If you start demolishing whatever constitutes as indoors while being careful not to cause large dust clouds that could obscure visibility, you could investigate the facility while also providing more materials to keep the solution working. And-
Wait a second! I just thought of something important while thinking about ways my solution could fail. There is snow entering the dome! That means you have a way you could try to escape through! And if that fails, assuming Steve is monitoring the site (or that you set up some monitoring equipment like Nik said you would), you could use it to send a message to the outside world.
Another thing, there are a few things quite commonly used in horror films to pass along information about an off-screen event. Piecewise might be nice enough to hand one to you if you search hard enough, but it might be better to look for one.