Tea and coffee are the only things that we're commanded not to drink, Dream Angel, when it comes to the "hot drinks" category. My understanding is that this applies regardless of whether the tea or coffee is hot or cold.
Many Mormons won't drink caffeinated soda. It's not served at BYU. A few Mormons forgo chocolate and other sources of caffeine as well. Most Mormons won't drink decaffeinated coffee. Many Mormons will also avoid eating things flavored with coffee, like tiramisù. Of course, all this only applies to Mormons who want to follow the Word of Wisdom all the time.
The only reasoning I've heard for these substances being off-limits is that the stimulants in them (caffeine and the rest) make it so that our spirits and our bodies don't interact with one another properly. They weaken us spiritually. I first heard this reasoning in the Brigham Young manual, but it's been there in later manuals in the Teachings of the Presidents of the Church series as well (those are the manuals we use in Relief Society and Priesthood). You can access those manuals
online, of course, including all the older ones like the Brigham Young manual.
Here's a paragraph on the topic from the Brigham Young manual:
"Instead of doing two days work in one day, wisdom would dictate to [the Saints], that if they desire long life and good health, they must, after sufficient exertion, allow the body to rest before it is entirely exhausted. When exhausted, some argue that they need stimulants in the shape of tea, coffee, spirituous liquors, tobacco, or some of those narcotic substances which are often taken to goad on the lagging powers to greater exertions. But instead of these kind of stimulants they should recruit by rest. Work less, wear less, eat less, and we shall be a great deal wiser, healthier, and wealthier people than by taking the course we now do. It is difficult to find anything more healthy to drink than good cold water, such as flows down to us from springs and snows of our mountains. This is the beverage we should drink. It should be our drink at all times.
It may be remarked that some men who use spirituous liquors and tobacco are healthy, but I argue that they would be much more healthy if they did not use it, and then they are entitled to the blessings promised to those who observe the advice given in the Word of Wisdom (
DBY, 187)."
Source