How long does it take for an orchid plant to rebloom? The answer is: it depends. I’m not trying to avoid your question, just being truthful. The truth of the matter of when an orchid will bloom again depends upon what kind of orchid it is. Most orchids will produce blooms once a year but there are some which are capable of producing blooms several time a year if the growing conditions are just right, if not quite right they should still bloom once a year. Since your orchid was in bloom last Christmas, my guess is that it should do so at that time again.
Since it is already October, if it were to bloom at Christmas time this year, it should be showing evidence of a new flower stem growing. But, depending upon what kind of orchid you have, it can take from one month to six months for a new flower stem to be in full bloom once it begins to grow.
On most orchids, once the flowers have all died and fallen off, you may remove the stem by cutting it off down near the base of the flower stem. Prior to cutting off the stem, take a look at the top or tip of the stem to see if it has begun to dry, if it does start to dry that means the stem is dying and may be removed. If there are any bulbs on the orchid, you should leave them alone as they are a store of moisture and nutrients for the orchid.
Most dendrobiums are not that hard to grow but getting them to bloom reliably is the hard part. Moving them to Florida will make it easier. Why? The climate and sunshine it will receive all year round rather than the cold darkness in Indiana. Dendrobiums prefer warm bright weather, they will sulk and even die under cold dark conditions.
From your description of them, I take it that they are of the evergreen family of dendrobiums. If they were from the deciduous family you would have mentioned that some of the growths had lost all their leaves. The primary difference between the two families is that evergreens do not like dry conditions while deciduous ones need a pronounced dry period.
Why your evergreen dendrobiums have not rebloomed for you is in what you said "Since it is so cold and dark here in Indiana". Whether in Indiana or Florida, place them in a location with bright indirect sunlight, temperatures between 60 to 85%F, humidity above 50%, light air movement around them. A good way to tell if it is getting enough light is to look at the leaves, they will be a medium green color when it is just right.
A word of caution if you take them to Florida, move them into any new light conditions slowly over several weeks, as too sudden an exposure to brighter light may cause sunburn of the leaves. If possible, try exposing them to temperatures in the mid 50%F’s for a month in the fall, that may help trigger them into the bloom cycle.
If, by chance, the leaves fall off, leave the growths on the dendrobium as they are a storage mechanism for moisture and nutrients. Only remove the growths that appear to be dying. As for those new growths, they may appear to stop growing due to the cold dark weather but should perk back up once things warm up and they receive more light.
You do not have to wait for a bloom to identify the type of orchid that it is if it is one of the more commonly available orchids. The most common is "phalaenopsis" that has large roundish to oblong leaves at the base of the plant and the flower spike grows from the apex of the leaves. Other common types are "the dendrobium, the lady slippers, and the Cattleyas". Each has a distinctive vegetative structure. If there was no tag with the plant, then I’m afraid there is no way to know the name of the hybrid since so many different hybrids have similar flower types and colors.
There are three principal types of containers for orchids. Phalaenopsis and lady slipper orchids are usually grown in a plastic pot, the heavier or more top heavy plants such as dendrobiums or cattleyas are better maintained in clay pots. Baskets are reserved for vandaceous orchids and require a very humid environment because the mix dries out very quickly. I would use a commercially prepared orchid mix that you can buy in bags at garden centers and mass marketers. I would soak this mix overnight before using it and drain it well before potting up your orchid plant in it.
Orchids that have maroon leaves generally get that way from having grown in bright sunlight. That suggests to you that either it was neglected or it likes bright light. It is not uncommon for orchids to outgrow their pots. Many feel this is the time divide and repot the plant, but that is personal preference. Many orchids do just fine hanging way out of the pot.
Since I don’t know what type of orchid you have, I can only hazard a guess that they are roots emerging from the pot drainage holes. Some orchids send out bloom spikes from the base of the plant but those are potted in baskets not clay pots.
For now, if the plant looks healthy,I would leave it as is until you get a further development such as flowering, plant die back, new growth starting,etc. Orchids put on new growth once a year and usually, but not always, in the spring. Just keep an eye on it and it should be fine. Then you will be able to know what type of orchid it is by the bloom. If not just go back to where you got the orchid and see if they know what type of orchid it is.