This train of thought reminded of me of my first car and a problematic starter relay that would only activate (and let the car start) when it was cold. As it warmed up from engine heat, the contacts inside got a hair bit closer and the relay wouldn't work until they cooled down again. I wonder...
No idea. Perhaps if the fluid was contaminated (say, with water) and is more prone to freezing? Probably a bit of a stretch...
I did find this thread, with a similar issue on an LX470: 98 LX470 AHC Suspension-->Cold Weather -...
I've no idea whether temperature would affect the pump. I suppose it could affect AHC fluid viscosity, which would affect the amount of "effort" the pump has to put in, and if the pump is weak for whatever reason, that could result in the problems you're seeing.
When my pump was burned out, the...
There is no reason for the pump to go bad in 25k miles. Many people on the 100-series LX run those pumps well over 200k miles without issues, and the 200-series AHC is more robust in every way.
The key to keep in mind is that the AHC pump is NOT self-priming. That means if the pump is not...