Is it possible to have a cat that goes outside AND not have a filthy house?

[iwouldgoouttonight]

Or am I going to have to wash her dirty muddy footprints off the floors, walls, duvet cover, windowsills, etc EVERY DAY????!!

Ah well I hate to tell you but it's not just the mud. My cat is fluffy and everytime he walks in the door he sheds a layer of dust, twigs, leaves or whatever else he's been lying in. He also brings in old feathers and things as 'presents' for me.
If you are like me and catflapless (ie have to open the door to the pitiful cries every 10 mins or so), you can minimise it a bit by keeping an old towel near the door. When my cat comes in on a wet day he now flops on his back and waits for me to dry his paws!

my bath tub
kittens out on THRUSDAY THANK GOd

We have a cat flap - tried leaving it closed but ended up letting her in and out every ten mins like you say! Have big mat near door for her to walk on to try to get rid of some dirt but she just jumps over it!