First off, welcome to AF!
I'll address the symptoms separately:
Shaking can be caused by many different things. Does the shaking stop after the car shifts into a higher gear? Does it gradually go away? Does it get worse as speed increases? Does it stop or get worse when you step on the brakes? Is it worse when you are turning left or right? I know it's a lot of questions, but pinpointing when it shakes can help deduce what is wrong.
A whining noise while turning usually means your power steering fluid is low. Your Camry probably uses Dexron III automatic transmission fluid (ATF) for the power steering fluid. Check the reservoir level and add as needed. If it is completely empty, you likely have air in the system and will have to work out the air over time...check, fill, drive, repeat. If it's been run low for a long time, a power steering flush wouldn't hurt to get the old, overworked fluid out. If that doesn't stop the whining, then the power steering pump may have been damaged from running the system on empty too long.
Smoke or steam while at a standstill are two different things burning...oil or coolant. Each smells different when burned...oil is acrid and coolant smells sweet. Common oil leak places are the valve cover gasket and the oil cooler hose o-rings inside and just underneath the oil filter. You'd see oil dribbling (or its remnants) down the front of the engine from the oil filter base...I know because it's happened to me...easy and cheap fix but the seals you have to get from the dealer. From the smoke you describe, my bet is on an oil leak from here.
Common coolant leak places are the upper radiator hose to the block on the driver's side. If you see leakage on the passenger side near the wheel, you may have a dying water pump. Also, there is a small coolant tube that goes up to the throttle body. Whitish deposits on the engine just below this indicate a leak there.
The cold weather can affect the power steering since it isn't warmed up by the engine directly, so it can feel sluggish until the pump's shearing action can get it warmed up.
Hope this helps!