I think there's a few games a 3 year old would play ... easier than musical statues/chairs etc is dead fishes where they have to lie really still and the one who stays the most still wins.
Or at my dd's nursery they play a game called the bean game, where you shout out which bean they should be and they have to do it - runner bean: run around, jumping bean: jump up and down, baked bean: curl up into a ball, broad bean: lie down with arms and legs out, french bean: shout "ooh la-la". Great fun - they love it.
And she also came home the other day telling me they'd been playing "What time is it Mr Wolf" - do you remember that? So that's another game.
You don't have to give them prizes, just a few games to get them playing.
Or you could make an obstacle course in the garden with cardboard boxes, cushions etc.
Something quieter would be get a load of paper plates, give them some crayons, ask them to do a self portrait ... then they can take it home with them.
And for a prize, you could hide them all over the house/garden, then give each one a really easy clue for their prize, so they can run off and find it.
As you can see, am thinking about my dd's next party so all this is in my mind at the mo!!