All waterbased glues, or paints are sensitive to low temperatures in liquid form and as setting, but so are a lot of other glues and paints as well, its notjust waterbased ones.
The problem with a waterbased polymer products is that the PVA or other polymer is not dissolved in the water in the bottle, it is tiny little droplets dispersed in the water.
Once applied the tiny droplets slowly join together as the water evaporates to form a continuous film of polymer.
In very cold weather the tiny droplets are too hard to join together as the water evaporates leaving a powder instead of a film, it depends how cold it is obviously, you should be fine at any normal tempertaure.
Aliphatic, PVA, acrylic, waterbased contact, waterbased paint and varnish are all like this
The mimimum film forming temperature of our PVA and aliphatic resin is around 3 deg C, many paints and some PVA`s are up around 8C to 10C some paints as high as 12C.
Its best never to freeze any waterbased product as well, most will not take any freezing at all , the polymer drops are destroyed as the water freezes and it seperates out, our PVA and aliphatic will take an average of 5 freezing to solid and defrosting cycles, this is very unusual for any waterbased glue. you can tell if the glue has ever been frozen as it will be runny water and solid polymer at the bottom of the bottle, this will not mix up and stay mixed if you shake it, once it seperates it is junk.
in general all chemical reaction type glues are slower but most still work, they take twice as long for every 10 deg C lower than room temperature, but once at 0C some tend to stop working such as laminating epoxy resins, most adhesive resins still set, CA is slower in the winter not due to the temperature, but due to lack of humidity on the surfaces due to low humidity in the air, there is a catylist in the CA to speed the cure with low humidity and low temperataure so you dont usualy notice the slow set in the winter with a CA
With our PVA, it has a secondary cure after it sets, to give the full water resistance, this is slower in very cold weather,in very cold weather you get high water resistance in a few hours after set, and full water resistance after a maximum about a week.