I didn't try to find out where you live, but I'm guessing it's somewhere cold! I agree that this sounds like an icing problem. Get the car warm and lube it well.

Since the pulling seems to move from side to side, it doesn't sound like a brake problem, although that can't be ruled out.

You can have several different problems with your brakes that can cause a car to pull to one side or the other; Worn brake linings are one, but you can USUALLY hear the metal-to-metal grinding noise. Not always, though!

Contaminated brake linings are more common; sometimes brake fluid will leak from the wheel cylinder and get into the brake linings and cause them to 'grab' unexpectedly. To cure this, you'lll need to pull the brake drums and look for signs of leaking brake fluid. It doesn't take very much to ruin a set of linings!

The only cure for this is to rebuild or replace the offending wheel cylinders, but you can sometimes save the linings themselves by soaking them for an hour in clean gasoline. Remember, if you set off a spark, your car and garage (and probably your house) will quickly go up in smoke. I've tried to use brake cleaner, but it doesn't seem to penetrate the linings to get at the contamination.

Plan on replacing the brake linings if you find a leaking wheel cylinder.

One rather unusual problem is getting ice into the mechanical bits of the brakes which can cause them to bind up. If you've been driving through water or slush, this may be your problem. Again, warming the car up will cure the problem temporarily. Make sure you have those little rubber plugs in teh holes in the backing plates to prevent this.

Also, consider your parking brake. If you set it at night and the car cools off, any water in the cable housings will turn to ice and may be causing one wheel or the other to lock up.

I still think the other posts here are on the right track; most likely ice in the steering linkages.

Good luck!