I travel a lot by car -often long trips .. how do you mums go to the loo with a baby too big for maxi-cosi??

My baby is no longer in a maxi-cosi-type car seat but is not yet walking. I hate to put him on the floor in public WC's for obvious reasons, but trying to do the necessary in a small and often ridiculously filthy cubicle (in winter .. ie with many layers of clothing!) whilst holding a big bouncy baby is pretty difficult! Do you have any tricks I haven't come across yet? Please ...??!!