If you are moving with a commercial truck (or plane), it may be too cold to transport them safely during the winter months. You might be able to have them crated in insulated packaging and then sent along with your household goods by a household moving company or possibly a freight forwarder; some courier companies will arrange very special transit including meeting a package at an airport and ensuring it is handled correctly or even accompanying a shipment, but this is pretty expensive.
If you make the move as stress-free as possible, your plants should adjust well to their new surroundings. More plants have been damaged by temperature extremes during transit than due to lack of light or water during the move. Continue to care for your plants as usual. On the day of the move wrap each one in sheets of newspaper to protect the leaves from cold temperatures during the trip from indoors to the vehicle. If they’re going into a truck or van, make sure they’re not squished together, to avoid bruising leaves. When you get to your destination unload them first and put them in a protected place, away from cold drafts. Once you’re all moved in, place them in spots that provide similar exposures to the light and warmth they experienced prior to the move.