IMO-
What axle to chain (1 pair) - Long term service, and for use at higher speeds rear tires. This is also the recommended position from OEM manufactures, on most modern vehicles.; SHTF- got to get through; Front axle, but beware on most modern vehicles chains can cause damage to front brake lines, ABS sensors, and other front end parts.
Best case - chain both axles.
Trailers - not necessary in most states; but California I believe requires commercial vehicles at times to chain one axle on trailers to keep them from jack knifing. Off road and forest service roads, I would think it necessary, unless you are driving off camber, and don't want the trailer to dog leg down hill when side grading. I would also consider if the trailer is extremely heavy, and it has brakes.
In my Jeep TJ I have two pair of traditional v-bar ladder chains, and I use them on average every 5 years to get through one of the Colorado Blizzards that dump on us. Usually to break trail through drifts on the streets that have not been plowed. When chained the Jeep tracks much better and it drives like a rock crawler slow and steady. Without the chains, you end up having to drive if faster to get through the same area, similar to Baja, and you drift a whole lot more. This is not a problem when you have the room, but attempting to stuff the Jeep through a drift between two abandoned cars can be a little crazy. As I mentioned before, if you need to do work with the vehicle chains are a vast improvement. In one storm I was needed to get a neighbors Super Duty unstuck. With out the chains the Jeep would go to the end of the pull strap and just spin the tires without moving the Super Duty. I put the chains on it, and was able to pull it up the hill freeing it. Nothing fancy, but the roads were just super slick.
For my Tacoma, I can only run chains on the rear, so I only have one set, preweg diamond chains. Have yet to use them, but it is nice to know that I have the option.
As for pulling a trailer in the winter I would carry a set all the time. The additional weight of a trailer can make it impossible for even a 4x4 to make it up small snow packed or ice covered roads. I can chain an axle in less than 10 min. and the amount of wear and tear on a vehicle, and the reduction of stress on the operator is well worth it. If you don't think you'll use them often buy a inexpensive set of ladder chains from Wal-Mart. A $100 investment is way cheaper then a tow truck, especially off road. If you have potential to use them more, upgrade to v-bar or diamond chains.
I like tirechains.com - purchased a set for a road grader, and a van this year for work, and I still saved money having them shipped compared to local vendors.