Freewheels are stupid simple--they lock when you're pedaling and spin when you stop. They don't care about the attitude of the bike.

If the problem seems to away after the top of the hill, and you know the wheel isn't rubbing on a brake pad or a chainstay, I'm going to bet on a broken hub axle. Remove the wheel from the bike and remove the quick release skewer from the wheel. Now, holding the ends of the axle in your hands, spin the wheel. If it spins OK, then I have no clue for the moment. But I have a hunch you're going to pull the ends of the axle right out of the hub.