Questions about Propagation of Dormant Root Crops and Winter Weather

So, I bought captors, a head of garlic, a tiny piece of ginger root and had some about to sprout potatoes from my last shopping trip.

In central Oklahoma, it gets cold to freezing until mid April.  

I planted the ends of the carrots, about half of the bulbs from the garlic head give or take and the piece of ginger root.  Will they be all right outside in their pot until they start growing in the spring?

I also have some whole wheat seeds, can they and the potatoes hang out in the shed outside under cover until spring?

Garlic.. plant it now and leave it outside, it needs to get cold over winter or it will not form bulbs next year, so yes that is fine (more than fine) outside
Ginger.. needs to be kept frost free so no it will not be ok outside, I donn't know how warm you get in summer but here that is a greenhouse only crop and even then we don't get long enough summers for it.
Wheat seeds, yes they will be fine so long as it is dry in the shed
Potatoes, must be kept frost free so a shed is probably not good enough, you may well be better eating those ones and buying new closer to time
Carrots. Do you mean you planted the tops of the carrots? They will probably die, they may manage to produce leaves and flower but they will not grow new carrots. The best you can hope for is for them to produce seeds you can plant the year after next.

While garlic is best planted in the fall, it is okay to plant soft neck garlic in the spring as well.  That said, I'm in agreement with @Skandi, I'd plant the garlic now and I agree with the advise about the ginger and carrots as well.  The shed is a bad place for your potatoes, but you can try your hand at planting the potatoes in the ground now (I would mulch them if you do) and they may or may not come up next spring.  If you don't want to take chances, like @Skandi said, you may as well just eat them and buy (certified) seed potato in early spring next year.  Also, if you decide to put the wheat in the shed, I would make sure that you put it in a tight, pest proof container.  If you don't, I'm sure the rodents might be grateful.

Ginger is a real challenge here in Central Oklahoma.  I've been working on it for several years, and I have some growing plants after many efforts, but it is not happy in this climate.  It wants tropical conditions at every stage of its life cycle -- warmer than 80 degrees, very moist air, and not much exposure to wind.  

To start with, much ginger root that you buy from the store will never sprout at all.  "They" say it's been sprayed with a sprouting inhibitor chemical, so buy organic; but my experience is that the organic stuff often won't pop shoots either.

So, for starters, don't plant roots unless you find them already popping the green knobs of new growth before you buy them in the grocery store.

I then discovered that "room temperature" isn't warm enough for young ginger plants in the wintertime.  If your house is at 72 degrees, moist soil will be a few degrees colder due to evaporation and whatnot; your ginger will rot long before it sends out new roots.  Just not warm enough.

I had to put an electric blanket under an empty fish tank, and keep my ginger starts in the (covered) fish tank with an open bowl of water also in there, just to get a mini tropical hothouse situation to get the plants started.  

They want to be moist but if the soil gets too wet, and especially if it is too cool, the ginger stems will rot and the plant will die.  

Plants grown indoors like this are exquisitely fragile and very difficult to "harden off" so that they will survive when taken outside into Oklahoma spring or summer conditions.

I had some in a tub interplanted with mint summer before last, that survived the trip outside.  They grew very poorly in the dry windy heat that prevails here, but they did survive the summer.  They didn't produce/enlarge their roots though.  

I took them inside and kept them all winter in a little artificial enclave I have indoors that's warm and brightly lit with LED lights, including some plant lights.  About half of them rotted off and died because I messed up the watering and  their soil got too damp or cool or both.  

The survivors I planted outdoors this past summer in a metal pot, very well drained.  This year they put up a lot of foliage, but still did not increase their roots.  They are back inside; but once again, only about half of them survived the transition and I'm by no means certain any will survive the winter.

Ginger is hard, here.  I hope to figure out a situation and method to get some plants to explode during the summer and make some fat roots.  But I'm like, four years into the effort, and I haven't managed it yet.