What is the impact of cold temperatures on glue joints?

The usage guidelines given for glues may be conservative (like those provided with finishes tend to be) but you can't have confidence in joints done using a glue below its minimum stated temperature; where strength is important err on the side of caution.

It's not like PVAs won't glue at all when it's cold, but strength can be severely compromised as any quick tests done in the home workshop should confirm¹.

We need some numbers, what temperature is the minimum it's safe to work at? It'll vary from glue to glue, so every user will need to check for themselves. But I'll give examples from Franklin Adhesives, makers of Titebond, since that's possibly the most popular PVA in the US market and in use around the world.

• For Titebond III:
  To assure a good bond, 45°F is the lowest recommended temperature of the glue, air and materials during application.*
  _{45°F = 7°C}

And note this is the minimum, the basic guideline temp is "above 47°F" (8.3°C).

• For Titebond II:
  To assure a good bond, 55°F is the lowest recommended temperature of the glue, air and materials during application.*
  _{55°F = 13°C}

For Titebond Original it is between these two temperature, 50°F (10°C).

Warm the project?
Warming both the glue and the wood seems like a good idea, and it is in theory, but it may not be practical inside the workshop because it's not enough to just raise the temperature of the room before you start work. Because, as we know, wood is a poor conductor of heat.

As a result it takes quite a long time for wood to warm up fully. And a warm surface alone may not be enough to ensure the PVA dries and then cures properly, plus the glue itself in its bottle will take ages to reach the ambient temperature just sitting in air². So really you'd want to warm the working area up from the night before. Ditto if you move the wood to a warmer place.

Switch adhesives
You could seek out an adhesive that's less sensitive to lower temps. This seems like the ideal solution, but the news is still not great.

The original Gorilla glue is apparently suitable for use down to 40°F (4.4°C). Other foaming polyurethane adhesives may be similar or they may not, you will need to check their packaging or the manufacturer's website.

In my case when the temperature drops too low to use PVAs and the project can't wait that means I reach for epoxy. Epoxies as we know cure via a chemical reaction between the two components, more slowly at low temps and faster at higher temps, but they do still cure down to surprisingly low temperatures (in case it needs to be spelled out, if you leave them long enough). When I use 5-min epoxy in a very cold workshop (below 5°C, 41°F) I make sure not to disturb the item for at least 12 hours³, and don't subject it to any strain for a day at absolute minimum.

An advantage of using epoxies at these temperatures is that the working time is quite a bit longer than normal, which is nice, but the long wait for it to cure can be a pain.

Rely on joinery and/or fasteners
Nails and screws don't care what the temperature is :-)

That's a bit limiting of course, so winter time is perhaps the ideal time to practice joints that don't rely on glue, e.g. tusk tenons and drawbored tenons. Also anything that inherently holds together such as lock mitres, and dovetails naturally, which can then be secured with pegs, dowels or brads that are inserted in such a way that they physically prevent the joint from separating.

This same principle can be extended to joinery that doesn't self-lock such as finger/comb/box joints, which can be locked together using dowels/brads driven in from both directions, even better if used dovetail fashion (at opposing angles) and stronger still, diagonally across the joint. Another option is a through peg running vertically through the fingers.

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¹ In one test I did on a particularly cold day I was able to easily separate two lengths of plywood glued at their ends, barely disturbing the surface veneer (a few fibres came off). Normally you would expect the veneers to almost fully peel from the next ply because PVA joints, if done right, are noticeably stronger than the factory glue joints in plywood.

² If you need to warm a bottle of glue, or finish for that matter, and you can't wait hours place it in warm water!

³ So no taking clamps off, or even moving the glue-up if it's heavy.