Another factor is can you control the temperature in your transportation? Yes, your car has heat.
What if something happens, accidents, traffic issues, heater malfunctions? These are all things to take into consideration. Your body heat may not be enough.
We talk a lot about travel cages around here. Yes, emergency personnel MIGHT look for an animal cage. There is no guarantee. But what will they do when they find it? Will they know it needs heat? Will they know who to contact to reach someone for YOUR information? Will that person know what needs to be done for your animals care?
These are not things specific to hedgehogs, cold weather isn't really good for you either. Being stuck in cold weather can suck.