Went out over lunch break to a nearby private pond (about 7 acres) here in central MO. I was only out for about 15 minutes before I had to come in. My braided line was freezing to the rod guides and to the levelwind on my reel. Guess I'll wait for it to warm up a bit.

You can try putting a lubricant or vaseline on your guides, should prevent the line from freezing to it. 

Hm that may be an idea.

When you're fishing in these conditions in the future, don't leave home without a can of reel magic.   Every so often hit your reel spool and line guides on your rod with a squirt of the stuff.

Try spraying your spool of line with KVD Line Conditioner. Spray the guides as well. And remember, the water is always warmer than the air is, so if you guides freeze up on you, dip the rod tip in the water for a few seconds. Will free it of ice, if for only a cast or two.

Rod guides freeze up because the line you are using holds water. Some years ago I lived in Idaho and this was often a problem One of the old timers there suggested Power Pro braid. I tried it. Problem solved.

Braid is not ideal in subfreezing temps. Not much you can do about it. Mono / fluorocarbon / copolymer will be a little easier to deal with.