My apologies if this gets covered a lot.
Yesterday I was riding and there was a light layer of snow of the ground. It wasn't enough that the bike couldn't handle it, but in a couple steep sections where I had to walk, my cleats got completely clogged with ice. I ride SPDs and would like to keep them because I can use the same shoes for my mountain bike and my touring bike. Is there a way from preventing ice from building up on them? I was wondering about the wax you put on XC skis for spring skiing or if something like WD40 would work.

Hard to prevent, other than never dismounting.
I keep one of these handy on all rides in the winter time to clear my cleats before hopping back on:

I don't even know what that is. I just grabbed a convenient stick.

It's a tool that's made to open cans of paint. They're usually free at home centers.

This is one of the reasons i switched to frogs. The cleat shape forces the snow and ice out when you clip in,

I run XTR Trail pedals for the Teflon coating. They shed ice and snow very well. I also spray the cleat area of my shoes with PAM every couple of rides.

I switch from my SPD to other pedals for snow/ice rides.
Some good winter pedals: CB Candy, Time ATAC, Look Quartz, any pedal w/an open design to help bust out/shed the ice/snow.