Without understanding of what tire properties can (and cannot) do for you, the principal effect of four wheel drive is well known to be:
"They allow you to get stuck deeper, so that it takes a bigger tow truck to get you out."
Used knowledgeably, (a rather rare happening) they can allow you to get around in more difficult conditions.
Whether the 2WD vehicle is front or rear drive, the most dangerous handling condition while the vehicle is moving is when the rear wheels lose traction. If you are moving forward, loss of traction on the rear presents a very high probability that the vehicle will "swap ends" in an imitation of what old-timers in my area called a "bootlegger's turn."
For this maneuver, preferably done only on dirt/sand roads where traction is not perfect, locking the rear wheels while at "escape speed" (by stomping really hard on the parking brake) results in an immediate 180 degree pivot so you are facing in the opposite direction while the pursuing rev'noor zips past you. Properly done you'll also decelerate enough to regain traction to make a "J-hook" mark on the roadway and can then go on to deliver your goods while the pursuer looks for a place to turn around.
The earliest front wheel drive vehicles tended to 60/40 weight distribution, with 60% of the vehicle weight on the front axle and 40% on the rear. The light rear axle loading made many of them quite prone to doing an "end around" with even a light touch on the brakes if the traction was poor. On ice, crossing a ridge in the tracks left by other vehicles could "detach" the rear, resulting in lots of sideward slides, usually off into a ditch.
There has been some improvement of weight distribution in more recent FWD vehicles, to put a little more weight on the rear axles, but the more important change has been "proportioning" of the brake systems so that very little braking effect is applied at the rear axle, and nearly all is to the front.
The "improvements" do not change the simple physics, and it remains true that in most situations the traction available at the rear of the vehicle is absolutely the most critical factor in handling (trajectory control, for many of the *&#! "drivers" around you) while you have some forward speed.
Unless you realistically plan never to exceed a speed from which you will coast to a stop within one length of the vehicle without braking, under all conditions you may encounter you need traction on the rear wheels at least comparable to what you have on the front.
If you need snow tires on one axle, you really need them on both axles. If the front "breaks loose" you normally will proceed in a fairly straight line in your original directiion, with some increase in stopping distance. If the rear comes loose, you have virtually no control over what direction the vehicle will go.