You never mentioned what temperatures...
Laminate wood is tough stuff. Dimensionally it is very stable. The grains of plys running across each other add strength. You aren't taking a thin solid wood instrument outside. I don't worry about my Flea and cold. It's gone camping with large temp swings and aside from having to retune it nothing has happened.
With solid wood instruments cold alone isn't a concern. As others have shared, it's quick changes that one should avoid. Both cold and heat can be dry. So you need to be aware of what the ambient humidity level is like outside compared to what it is like where you store your instrument - not paranoid about it, but aware. You may need to bring a case humidifier to help mitigate humidity swings traveling to and from the gig (in the Pacific NW you may need desiccant packs or something similar to absorb humidity...).
Cold causes items, including instruments, to contract. This will make instruments go out of tune as the item contracts. Expect this and plan on checking the tuning.
Quick changes from hot to cold, or cold to hot, cause the instrument to contract or expand rapidly. This can cause problems. Different materials contract and expand and different rates. If done too quickly the materials may fight against each other as one contracts faster than another. In such a case you might see things like gloss finishes crackling over time and repeated quick changes.
With large temperature differences, always bring a solid wood instrument in and out of extreme environments gradually. The wider the temperature difference the more you may want to watch this (house to garage and let it sit for a while, garage to car truck, etc.). Use a case. The case will help mitigate quick changes by providing some insulation, and help the instrument warm up more gradually.
I used to set my bagpipes (in their case) out in the inslutaed but non-heated garage for a while if I knew I'd be playing outside in the cold (40°-45° F). This gave the case and instrument time to cool down slowly. Then I'd transport it in the trunk of my car because it would not be heated.
When I came back I'd put the case in the garage for a while to warm up, then move them into the house and leave the instrument in the case until the case warmed up. Finally I'd open the case, but leave the pipes in their foam holder. This let the inside warm up, but the foam was still some insulation.
Solid wood bagpipes are more expensive than laminate ukes, and as the solid wood ages a wonderful tone developes, so this amount of work was worth it to me.