Well, since most of the body heat loss comes from your head, you should do your best to cover that completely.
I reccomend using the plastic trash bag for this purpose. Tie the opening firmly around your neck, as you don’t have a scarf, and the neck must be kept warm too.
Then, stuff your clothes full of leaves. This will increase their insulative ability, and add padding for when you lie down. Put leaves in your shirt, put leaves in your pants. Put leaves in your coat. Put leaves in your socks, and leaves in your shoes. Fill your pockets with leaves. Put leaves in your undergarments. Be sure to fill all available nooks and crannies with leaves… don’t forget, the armpits and crotch have substantial leaf storage space! Every bit helps.
Finally, wrap the wet blanket around yourself as tightly as possible (to prevent further heat loss) and lie down underneath the tree.
Then wait.
In about ten minutes, you won’t even notice the cold anymore!
Serious answer so I don’t get banned if some idiot actually takes the above suggestion:
Ditch the blanket. If it’s not freezing, that water is gonna evaporate, and evaporating water is COLD.
Of course, if you’re thinking very long term, just hang the blanket from a tree. In a few days it will be dry, and then you can use it. But overnight? Dump it.
The OP doesn’t mention if it’s raining, or if rain is likely. I’m going to assume that rain is expected.
In this case, your primary goal is keeping yourself and your clothing dry.
So, keep yer clothes on. Put the coat on over them. Assuming the coat is not waterproof, poke a hole in the garbage bag and wear that over the coat. DO NOT poke arm holes. You won’t use your arms… they’ll be huddled up in your coat, keeping you warm, and armholes are just more places for water to get in. You’re gonna get wet enough through the neck hole, you don’t want any more wet than you can avoid.
If you really want to, you can stuff your coat with dry leaves for a little more insulation. It won’t help much, if the coat is any good at all. Do this on the outside of your shirt to avoid itching.
Since the blanket is gonna stay wet a while, you can try to fashion some kind of shelter with it by hanging it from the tree or whatever. It couldn’t hurt.
Then, you need something to sit on, unless you plan on standing all night. The ground can suck the heat right out of you at night. A pile of sticks and leaves makes a passable bed. More leaves on top can keep some of the wind off, and function as a blanket of sorts.
If you survive, find Prometheous… if the coat is a good tough leather, he might just trade you for some matches!