I lost all of my antifreeze and car started smoking

hi there.
this will help you find out if its your tires thats at fault.
https://www.lesschwab.com/learn/article/what-to-do-when-your-car-is-stuck-in-snow
or read up more at this link.
how to get traction in snow Google Search

Black smoke is fuel. One or more of the fuel injectors could be stuck open and when you shut it off, the fuel drips into the cylinder. When you start it, that extra fuel burns and blows out black smoke. Blue smoke is oil and white smoke is antifreeze/water.

water pump maybe?

White smoke is most likely antifreeze from a leaking head or intake gasket.is the oil milky looking and over full level? Is the antifreeze milky or low or coming out the overflow tank?

gas may of froze in fuel line do you have deicer in the tank

WHITE SMOKE MEANS ENGINE IS BURNING ANTIFREEZE.TURBO WILL SMOKE HEAVY BLUE WHEN TURBO SEAL FAIL.ALSO YOU WILL LOSE POWER.YOUR CAR IS TOO NEW.TO HAVE PROBLEMS.YOUR CAR SHOULD BE WARRANTY COVER.TAKE IT TO SAAB DEALERSHIP.LET THEM CHECK IT OUT.

When you got stuck in the snow did it impact hard (quick stop or small drop like a deeper ditch)? If this is the case it could be the sending unit might have been dammaged in some way. I would have the shop take a look at.

Perhaps you have a partially frozen fuel line from sitting in the snow bank. Pour a bottle of gasline antifreeze in it for now, just to see if that may help. It may only be getting enough fuel to idle, but not run when accelerator pushed. Hopefully if that is the problem, the antifreeze will work it's way down the line enough to get you out of there.

my wife has the same car we bought it new. the computer has gone out three times on it, the traction control does not work, and we live in wisconsin so it wont spin a tire in the snow. The remote start stopped working this winter also. The car is a total pile of ****. we also have an 04 grand am. when it snows more then 2 inches i cant even move the g6 out of the drive way because it will get stuck while the grand am will go through just about anything. my advice to anyone who has a g6 dump the p.o.s. Mine is being traded in on monday after getting stuck in the driveway again tonight after 2.5 inchs of snow. FN G.M. junk!

Take the car to Autozone, they will read the codes via OBD II for free.  Other parts stores may have the same policy ... call first.   My VW dealer charges $40 to pull the codes!!   I bought a low-end OBD II reader for $50, as the wife and I  both have VWs.

White smoke is usually antifreeze, the most frequent cause of this is head gasket blown or cracked head ... big bucks.  Hopefully this is not you.  Unless the car had a dramatic overheating incident, for most makes of cars, this should not happen until you have over 100K miles, probably closer to 200K.   
White smoke could also be break fluid sucked in from power brake booster.  If it's brake fluid, it will smell very bad.  
On cold days, when the car first starts, white smoke can just be normal condensation in the tailpipe ... if it happens after the car is warmed up ... it's something else.
Check your coolant overflow tank level ... if it's very low or empty ... put water in (don't bother with antifreeze yet in case you are burning it up in the engine).  
Good luck, ..ajm