I came from a hiking background like yours so I can relate.
I have not done South and Central but have done Odells and Pinnnacle. People use protection on ice if they feel they need it to be safe because of the technical difficulty of the climb or the condition of the ice.
As you are starting out and may not have a good "feel" for ice and your comptence on it, it would be prudent for you to bring protection for these and use it as you feel necessary. Personally, for there, I always bring 10 or so ice screws, some rock gear (a few stoppers, 2-3 tricams, and maybe a couple of cams), and 3 or 4 pitons. This may seem a lot (for South and Central especially) and opinions will greatly vary on this, but, when you need it you need it. I always climb faster (and have more fun) when I feel I am well protected. Steve House I am not!
People solo these and they are technically easy but you should treat them as technical climbs. Learn how to place protection. If you want to test the system and yourself it might be best to do something like Willeys Slide first. The approach is easier, committment much less, for the first time you can always climb close to the side for an easy escape if needed, and all you need are ice screws, no rock gear. Shoestring Gully would then be good second climb.
Don't be too swayed by what others do. It is your life. When I first started my first "lead" was on the trestle slab at frankenstein where we rapped the slab and preplaced at least 8 screws. You cannot imagine the caustic comments we got from some.
Having said all this I have been thinking of some time to try Hillmans Highway in Tucks. It seems to be a pure snow climb. Skiers do it. I would not bring gear for this. I would think it best to wait for a heavy snow cover to reduce bush wacking and watch the avalanche report! This might be fun but as i said I have done it so can't comment personally.
I bet I am 1 for 3 on Huntington Ravine, now, if I read the forecast is for winds over 50 mph with temps 20F or below I don't even bother with it, I go up Lion's Head to taste the beast or go someplace else