My cat is very weak and not moving, accept for his head in an erratic way. The area I live has been hit with 6-12 inches of snow, so not sure if we can take him to a vet right away. He does meow in a cry-out way of sorts?

Let your cat rest. Keep food that smells strong, like tuna and water and litterbox near by. Keep your cat comfortable like on a blanket and warm, but do not cover. Let the cat sleep as much as the cat can. Something could have happen. If the cat is purring and still meowing, could be hurt. Some animals purr for happiness and hurt. Animals have a way of recovering. If the cat does not eat, that is normal. Most animals do not eat if they are sick. Let the cat rest a few days and moniter. Pet the cat softly, to reassure that someone cares.

You probably should, or give it some water and food. Maybe thats why it is week, give it another 2 hours, if it does not perk up, take it to the vet

Check your cat all over to see if it has a tick. Check inside of its ears. See if the ears are dirty. If so it may have ear mites that can cause it to lose balance.