I would say you are fine. You'll get enough snow/rain to put it back to where it should be soon enough. The only issue you might have in the meantime is really high wind. If you happen to see a nor'easter/bomb cyclone/blizzard coming you can add 8 inches just for piece of mind and let mother do the rest.
The black strings are from my cover, it blew in a couple weeks ago, this is my second winter with the pool and it blew in last year too, might not bother with it next year, do you cover yours?It should be. What are the black "strings"? I wonder about adding water but am unsure what is under the snow so am holding off on suggesting that right now.
...you thinking there is a bad storm with winds it could possibly damage the walls because so much is exposed?
Yes. Exactly what I was thinking. It can act like a sail or parachute. Yours is still mostly full so It would take some really strong winds but any given Winter storm is only a few days away. Adding some water now like @Poolmedic said is certainly the safest bet. Putting a new cover on after the refill would be even better. Depending on your time and finances of course.
The above is bad advice, yes the water is weighing down the bottom but that isn’t the concern. The sides are vulnerable.
Wind. 8 inches of more water would reduce the exposed surface area by about half. Those walls are razor thin and can easily bend or collapse. In the picture it is fine on a regular mild wind day, but adding water would certainly be the safer bet.