Engine misfire, only when it snows

Sounds like a misfire , plug or coil breaking down . Does the check engine light come on or flash ?

Diagnose Engine Misfire - Auto Diagnosis Repair Help

www.aa1car.com/library/misfire.htm

The engine may shake so badly at idle that it causes vibrations that can be felt in ...The engine may only misfire and run rough when cold but then smooth out as ...

What is causing an intermittent misfire only when engine is ...

community.cartalk.com/.../what-is-causing-an-intermittent-misfire-only-...

Jun 27, 2013 - NOTE: You MUST restart the engine for the misfire to go away. ... in an expert to do that test, but it might be worth it to prove/disprove the injectors being thecause. 0 ... The first is that the car should run fine even on cold starts.

Engine misfires when cold but runs fine after warming up few ...

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Mar 24, 2009 - They also gave it to me because of this misfire problem it has. ...Engine misfires when cold but runs fine after warming up few minutes later? ... and you start next morning will also cause a misfire until it burns off the coolant.

"Miss/splutter" with cold engine, but fine when warm? M103 / also ...

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Jul 13, 2011 - My moms old 300SEL (with the M103) that was once my car is now my "work car" again as she is getting a brand new SUV very soon.

Cold start misfire solved (finally!) - Bimmerforums

possible couple of things
low battery voltage by the system not charging enough
overheating component in the ignition system--coil failing when hot
engine overheating- no air flow around head and cylinder fins from dirt and rubbish

Google search toyota forums and start reading.

P0316 FORD - Misfire Detected On Startup First 1000 Revolutions Symptoms - Engine Light ON (or Service Engine Soon Warning Light)
- Engine fails to start
- Engine runs rough Possible causes - Crankshaft Position (CKP) sensor harness is open or shorted
- Crankshaft Position (CKP) sensor circuit poor electrical connection
- Faulty Crankshaft Position (CKP)
- Ignition System
- Fuel Injectors
- Running out of fuel
- Fuel Quality

Timing is off,problem with timing chain,also check fluids in ******,plus also if you have a distributer in your vehicle,if it is cracked,moisture getting in and ruining the points,-that is if your vehicle has a distributer! This will make a vehicle run rough as well.
You can have new plugs put in,but if your spark plug wires are cracked or worn,this will also creat misfire and backfiring.

your torque convrtoer is shot. it is the at the front of the tranny to transfer motion from fly wheel ( engine side) to the trans. its a fairly cheap and easy fix.

Sounds like you have a bad spark plug wire. Start the vehicle, then take a squirt bottle of water and spray around the plug wires. You should find it. It'll look like static around the bad one. Also you should get the misfire. You'll probably find a worn area on the wire. Best wishes to you.

you need a new choke

First problem sounds like starter solenoid. Second is definitely gearbox mounting.