Car is stuck in my front yard and the ground is soft

No, even a 4x4 will have only 1 wheel that will spin on each axle in this instance. It's called a floating differential. For stock vehicles with non locking differentials like you have, both cannot spin or have full power at the same time. Hard to explain on this, but picture your car making a hard right turn. Both front wheels would be spinning at different speeds because of the turn. The passenger side tire is spinning much slower than the drivers side tire, therefore if both were spinning at the same time, your tires would chirp and skip on the pavement which would eventually ruin your differential. In offroad applications, we WANT the differentials locked and turning at the same time with true 4x4. But in normal everyday vehicles, even standard stock 4x4's, only 1 tire will do the spinning per axle unless it has possitraction or full locked axle. Clear as snow?

All wheel drive is just that-- All wheel drive-- not to be confused with 4 wheel drive . The difference is with AWD there is a 3rd diff in the transmission that allows the front and rear wheels to operate at different road speeds . When 4wd is selected that 3rd diff is locked and so both front and rear wheels drive at the same speed regardless of ups and downs in the road surface . This results in a torque wind up in the drive train and places load on "U" joints --splines --CV joints and gear teeth . The grinding on turning corners will be the CV joints trying not to flex because of the torque wind up . How to prevent this problem=== Do not use 4wd on hard road surfaces === as the tyres cannot slip to relieve the torque Restrict the 4wd use to snow , mud and loose surfaces TO fix the problem unselect 4wd drive and reverse several yards to release the pressure in the drive train and the actuator has a chance to pull the gear out of lock up. If that doesn't work check that the actuator is actually working

The answer to your issue most likely lies in the brand of tire. Kumho has very poor tread wear and often handles poorly in slick and snowy conditions. While their dry surface handling is generally good, and they seem quiet, that is about the extent of the plusses for Kumho. Sorry.

check all wire connectors for water ingress and tight. check that the snow has not allowed mud to get any where to hinder correct operation

check shifting rod see if damaged.

If there is pressure on the front wheels, it may prevent you from turning the key to get it out of park. Try turning the steering wheel to relieve pressure and try shifting out of park.

4WD is for soft ground or snow Do not use 4WD on dry pavemant for it wears out the transfer case 4 wheel drive gearing faster and the front tires out very quickly too

You say it got cold, but are the roads snow- or ice-covered? If you are driving on dry, hard surfaced roads in four-wheel drive (regardless of the temperature), you are putting excess wear on your transfer case and front differential, and yes, you can get some clunking, especially in tight turns.

when driving in 4wd engagement there is a problem in that the torque in the axles and drive lines is not dissipated on hard surfaces as the wheels cannot slip ( great for snow ice mud gravel and the like but a no-no on hard non slip surfaces
yes reversing it will relieve it but if on hard surface ,winds it up again in reverse
better to simply drive two wheels onto the grass verge of the hard surface and then kick it into 2wd
if the diffs are limited slip diffs then the antislip action in the diffs will be pressed very hard together and will produce problems on turning corners
you may have success if you get all 4 wheels of the ground on a hoist and let the wheels spin and then try to engage 2wd

Your rear brakes have failed.