Mice, in my experience, don't seem to be a great problem. The glue is applied pretty thin and unless the house is already overrun with mice I don't see see them pulling a mau-mau on your improvised window insulation.

Roaches will nibble the glue in time. The SE is big on roaches. I don't care how fastidious and clean you are every house that isn't soaked with pesticides has some roaches. You can limit their attraction to the glue by mixing in boric acid to make it unpalatable. But newsprint and flour glue isn't extremely attractive to roaches. Nor is it intended to be a long term solution. So if the roaches nibble the edges a bit it isn't the end of the world.

It is a short term survival strategy for sealing a house tight enough to stay warm in. And a stopgap measure for people with few other resources. In time moisture, roaches, ants, perhaps mice and mold are going to attack the glue and newsprint and destroy its integrity. With a little luck this happens slowly and after winter has passed.

I didn't mention it but it is also something of a fire hazard. If the newsprint catches it is going to go up fast because it is a thin section of flammable material held vertically. Curtains are also a hazard for the same reasons. Be careful and use common sense. Keep candles, heat sources and sparks away. Keep a fire extinguisher handy. If you don't have, or can't afford, a fire extinguished keep a bucket or buckets with water and/or sand handy.

Come spring you can tear it down and redo it in the fall.