Just monitor the relative humidity. The necks on a couple of my basses get a little twitchy if they get dry. During the cold winter season here, I keep little humidifying spongeboxes in the cases with each one.
100% this.
I ordered a double bass from Upton Bass right before the pandemic lockdown occurred, and when it was time for my bass to be shipped, shipping was so problematic and expensive that Gary Upton converted a Mercedes Sprinter into a camper and drove around the US delivering basses to people.
I received my bass in November and it was 20 degrees Fahrenheit (about -7 Centigrade) and my bass had been hauled in an unheated trailer along with the others.
While the absolute humidity was low, the relative humidity was just fine, and didn’t cause any issues with the basses being transported.
Only thing I had to watch out for is keeping it in the bag for a day so it could warm up. A very cold bass brought in to a house with decent humidity is going to get condensation which is really bad for uprights.