How does freezing temperature affect electronic equipment?
It really depends on the parts you have, especially with the IC and the motor.

ICs are always temperature rated and you can see their working range in the datasheet.
If an ICs gets to cold it can get fractures in the small inner structers, which can be as small as several nanometers and are quite fragile due to that. But a 555 will have no problems with -15°. The moisture is not really problem, except when you activly cool the chip below the temperature of the environment.

The motor itself will also have no problems with the temperatur, but you have to choose one which is (again) rated for that temperature range. The reason is that the lubricant of the bearing has to keep its greasing properties.

The batteries are the biggest problem. At -15°C they will have a strongly reduced chemical reaction speed, which increases the internal resistance a lot. You really want to keep them warm during operation.