Whats on the left side that could be makin a grinding noise,lots of snow and slush here lately.?

An axle....Ice built up in the area rubbing against it..a control arm ice on it rubbing around basically anything just get under it and see what you can see if any ice remove it make sure the boot on your axle isnt torn

if the car is not moving?

Snow and ice possibly built up around your torque convertor and flywheel

When you say left side do you mean drivers or passenger...if passenger could be around HB or any pulleys...If drivers the closest thing that moves when running is the above stated Tc and flywheel

left side is always drivers,i didnt know snow and crap could get in there..

It can slip past the inspection sheild

I would remove the inspection plate and look inside. When the car is not moving the transmission is not moving. Only the flex plate and torque converter. If ice got in there is will make noise.

Wouldn't the ice melt after so long?