Normally a compost pile only smells when it goes anaerobic. It's usually caused by adding too much green or too much water. It will still rot but it takes longer.
I am assuming it is wet throughout and not just in areas where there is a heavy accumulation of greens.
There should be no smell if it's fully composted.
As tomc says, you can go ahead and put it out if you feel it has finished. If it isn't finished soil bacteria will continue to work on it and consume nitrogen as they do. You'll get it back when they die but you may have to add nitrogen to the soil to compensate for the temporary loss. I do it all the time.
I agree with Rainbow, it's too late in the game to add sawdust.
First dry it out like imafan26 suggested. Then toss to aerate.
After a couple of days, if the smell doesn't go away, there are probably too many greens in the pile and you should add brown leaves. Did you count the horse manure as a brown or green? It's a potent green and it is easy to underestimate how much you're adding when it's mixed with straw.
If the smell goes away and it doesn't heat up, but you still want to try cooking it off, mix in some more horse manure. If that doesn't heat it up it's probably done as much it will.
You can either let it age a few months (because of adding manure that wasn't aged) then use it or add it a little at a time to your new pile.
I see by the color of your grass and bushes that it's warm enough to for a proper pile to start cooking.
Good luck and please let us know how this comes out.