How to prevent my disc brakes from locking/sticking due to debris? Context:

I have a commuter/crossover bike with disc brakes, and a daily commute of ~20km. I upgraded to a bike with disc brakes after standard caliper brakes kept losing their stick and requiring pad replacements, as my rims became coated with oil from the roads (I commute past a diesel truck depot, and the road is nasty for about 1km). 

Problem:

Since I upgraded, I have the opposite problem: literally every day in the winter, my disc brakes get full of mud, road salt, and sand. That stuff gets on top of and behind the (magnetically attached) brake pads, and makes them drag on the rotor. At best, they make the brakes constantly pull as if they were about 1/2 engaged. At worst, the water in the mud freezes and expands over night (I have a tiny apartment, and the bike sleeps outside), and the brakes are completely locked in the morning. 

What I've Tried:

At first I thought it was the cables that were freezing with tension on the brakes, but after replacing and oiling them, I isolated the problem to the brake rotors/pads themselves.

The roads where I live are pretty much always covered in debris all winter, so changing my commute to avoid that stuff doesn't really work.

I've tried adjusting the brake pads farther away from the rotors. This works a little, but to fully prevent sticking, I have to adjust the pads so far out that I can't fully engage the brakes when I want to.

Up until now, I've been washing the bike with water every night (annoying, since during the winter the outside faucets don't work), and rinsing the brakes with warm water every morning to unfreeze them. 

Question:

This is getting really old, so my question is: without obsessively cleaning them 1-2 times a day, how do I keep my disc brakes from getting gummed up? If the answer is "buy better disc brakes", that's fine. I just have no idea what to look for.
I think that cleaning with water is the problem. You wash them overnight, leave the bike outside. Water freezes inside of the breaks. You splash hot water again in the morning and get more water on your breaks and behind the pads that will freeze later on. 

I would try avoid using water in your daily clean. Just try it for couple times. Clean the pads with dry cloth and make sure there is no water in the system. And see how it works next day.

To be honest, I have never experienced this kind of problem. And I've used disk brakes for the last 10 years in very different conditions, including thin wet mud all over the bike, brakes and pads. And I never got mud between pistons and break pads.
So I think the problem with "magnetically held" pads. My pads always been held in place by a spring.

So if you have this option, try changing the breaks, but make sure that new breaks hold the pads with a spring, not magnets.