It would die of the shock from the cold! It is too used to household temperatures to do that to it until it warms up outside.
Your best bet to kill the bugs and not harm the plant may be to find some insecticidal soap, mix it according to package directions and wash the plant and drench the soil with it.
It is really important that your plant is packed well for the move...I thought that mine all were...but a really beautiful one flipped and was crushed and cold damaged by the time I found it. Somewhere on here somebody did a thingy on packing plants for a move....I couldn't find it, maybe someone else can help...
