Allow me a word about traction first:
A car needs traction for 4 things: lateral stability, acceleration, steering and braking.
4WD gets you 100% more traction than 2WD. Good!
We all know, rubber tires on snow and ice have very little traction.
So, in 4WD you get 100% more of very little. That isn't much!
It might be enough to get you over the snowy pass. Definitely it is not enough to be really safe. Only aggressive steel tire chains put between the tire and the surface of the road increase traction to a truly safe level.
Only tire chains increase traction of rubber tires on snow and ice significantly!
Back to the question, what happens when you mount tire chains on either front or rear:
On 4WD vehicles:
• Snow chains mounted on all 4 with 4WD/AWD - ideal lateral stability, perfect acceleration, crisp steering, super braking. However, part time systems will show some understeer (turns are wider than intended). Full time 4WD systems are best. This is what everyone should have for snow and ice. Be careful anyway.
• Snow chains mounted on front axle with 4WD/AWD - good acceleration, good steering, good braking. However, since the rear wheels have no lateral guidance, the rear end might come around - fast. Not good. Feather your brakes. Go slow.
• Snow chains mounted on rear axle with 4WD/AWD - good acceleration, lousy steering (no lateral guidance), marginal braking (remember, 80% of brake force is created at front wheels and without chains that ain't happening). No fishtailing. Best compromise for 4WD with only one pair of chains. Go slow.
Why you should have 2 pairs of snow tire chains.
Attention: Since some of the automatic AWD systems are marketed as 4WD or AWD, placement of snow chains has to follow different rules - check with your owners manual for correct procedure.
Here is more about the various 4WD/AWD systems.
Here is what happens when you mount tire chains on either front or rear:
On 2WD vehicles:
•Chains mounted on front axle (front wheel drive) - good acceleration, good steering, good braking. However, since the rear wheels have no lateral guidance, the rear end will come around. Not good. Feather your brakes. Go slow.
•Chains mounted on rear axle (front wheel drive) - almost no acceleration, bad steering, so so braking. No fishtailing. Not useful.
•Chains mounted on front axle (rear wheel drive) - almost no acceleration, good steering, good braking. However, since the rear wheels have no lateral guidance, the rear end will come around. Not good. Not useful.
• Chains mounted on rear axle (rear wheel drive) - good acceleration, bad steering, so so braking. No fishtailing. Not useful.
However, some states have their own idea about where you should mount your chains.