Not to derail the always amusing Spare Air rant, but back to the OP's question.
senseiern, you ask about adding gear to "improve your risk management". Risk management is a vital and constantly evolving requirement of diving... but adding gear is only one component. Managing risk, to me, is about a) preventing problems and b) solving problems. While adding gear can, at times, aid in solving problems... training will help you prevent problems.
Every diver has a limited amount of brainpower and can handle a certain number of tasks with that. As you train more and dive more, you become more comfortable, have to think less about each individual task, and can handle more. If you exceed your maximum task load, even if you are Jacques Cousteau reincarnated, you will drop tasks.
Personally, I manage risk by managing my task load. If a dive has the potential to require more tasks than I can manage, I will not do that dive. The beauty of a buddy is that they can, in an emergency, handle some of your tasks for you (e.g. entanglement)... thus reducing your load.
As a beginning diver, buoyancy, trim, air consumption, weighting, finning, and making sure that rental equipment is adjusted just right will eat up a significant portion of your task allowance.... just as it did when I and everyone else started. Then your instructor adds skills.
Adding a pony bottle, particularly a slung bottle, to the mix adds one more task for you to manage. In this case, particularly under the close supervision of your checkout dives, I would suggest that adding another task to your load will cause you more problems than the redundancy of an extra tank will solve.
After all, you already have a second tank... it's on your buddy's back. You know it's turned on and working because he's breathing off it and, because you're diving recreational limits, you're a CESA away from the great air tank on the surface if all hell breaks loose. Yes, there are horror stories about inattentive buddies swimming away... but if you notice there are very few stories about a buddy sticking close to you, then swimming away for the first time the instant you have a spontaneous OOG emergency. If you prevent the problem, by a) watching your gas consumption b) taking care of your gear c) inspecting it thoroughly before each dive d) staying near your buddy (the responsibility to stay together is the buddy team's... not one diver or the other's).... then solving an OOG becomes very easy. Remember, you're trusting yourself to avoid the problem in the first place; you're trusting your buddy to bail you out if you screw up.
A pony has its place... particularly in cold water as you allude to. There, if your first stage freezes, bailing out to your pony and shutting down your main tank quickly will often allow the water to warm up your first stage, letting you switch back and continue the dive. [Though strictly from a safety point of view, many advocate ending the dive as soon as you have to tap your pony.] In this case using a pony avoids increasing the demand and adiabatic cooling on your buddy's first stage, making it less likely to freeze in turn. It also requires you diving in pretty cold water, calmly switching regs amidst a flood of bubbles, and still keeping your breathing rate low enough to avoid over-breathing the pony reg as well.
Once again, I would suggest this is loading beyond your current task threshold... as well as much cooler water than you will want to dive at first.
To paraphrase TS&M, you can either dive solo or trust your buddies [and from her conduct and knowledge on this board, I would be inclined to trust her recommendation of buddies]. At this point, I would respectfully suggest you are not qualified to dive solo. If you can't trust your classmates, trust your instructor. If you can't trust your instructor... please complete your class somewhere else.
Once you are comfortable in the water and can manage the tasks you are likely to see currently (e.g. do a mask flood and clear while maintaining trim, depth, and swimming), if you still see the need for a pony, by all means add it. But right now I think you're overestimating the problems it will solve and underestimating those it will cause (particularly if you sling it).