Your best bet would probably be to get a storage box with a lid- make sure it's food-grade plastic. Staples used to do those really useful storage boxes, not sure if they still do but they are food-grade.
Then you'll need a battery-powered air pump (why do I always type 'pimp'? ) and some insulation if it's still this cold: bubble wrap or newspaper will do the job.
A lot of people use Stresscoat when they're moving fish, might be worth a go.
To move your filter I would put all the media in a bucket with some tank water and shove another battery-powered air pump underneath to keep the water moving. Hopefully you won't lose too much bacteria but you might want to get some ammolock or bactinettes ready just in case.
Finally I'd get a big water container (a fish shop should have them, 5 or 10 gallon) and save some of the water.