I didn't read a manual because I was test driving the Jeep.
That's OK. We, your fellow road users, commend your commitment to safety. Why, just the other day I saw a lady driving along the Interstate reading a newspaper while driving. Clearly she was lacking this same fundamental consideration for others. What a cow.
I've never owned a 4x4 so I am not familiar with it. The closest thing to a 4x4 I've driven was an AWD Outback.
HELP IS AT HAND.
There is an E-Z-2-understand overview of how Jeep's 4WD systems work on the Internet! See
http://www.jeep.com/en/4x4/how_systems_work/command_trac/ for a video covering the basics. Although a more recent video than the transfer case whose steering-binding abilities you just experienced, I can assure you that its information applies equally.
You may wish to compare and contrast this information with that available from Subaru, with whom you have some familiarity. See
http://www.subaru.com/engineering/all-wheel-drive.html for examples of how their system differs from that in the Jeep. Note that you can also lift and wheel a Subaru, so that may be an option for you to explore. We'll understand if it isn't one that you're interested in pursuing, however.
Can the 4H be used if there is A LOT of snow on the ground? Such as the blizzard like conditions that the DC area was hit with this year?
Absoutely! In fact, many XJ owners did exactly that this winter, and with great success. It can also be used on surfaces such as (but not necessarily limited to) sand, mud, gravel, and rocks. It is truly a miracle of modern automotive engineering.