I'm a believer in honey and cinnamon, but NOT for the reasons you've found. Here's why I incorporate honey and cinnamon into my diet.....
From the Whole Health Reference Library:
"Not only does honey add flavor to numerous foods but it is a sweetener that is relatively good for you. The only natural sweetener that requires no additional refining or processing to be utilized, honey is composed of 38% fructose, 31% glucose, 1% sucrose, and 9% other sugars, along with water and small amounts of vitamins, minerals and acids. Honey also contains small amounts of Amino acids as well as Vitamin B6, thiamin, riboflavin, pantothenic acid, and trace amounts of essential minerals, such as calcium, copper, iron, magnesium, manganese, phosphorus, potassium, sodium and zinc. Even though these substances appear in trace amounts, they do nonetheless contribute to overall nutrition intake."
I eat whole foods, and I do prefer to use honey in place of sugar when I can - but I still choose to use both as sparingly as possible. Just because honey has some health properties and antioxidants, I don't consider that a license to use it judiciously - a little in black tea, or sometimes on my toast or over some plain yogurt is about as far as I go. I do personally think that it's a better choice over sugar in your tea, but just be careful how much you're adding and how many cups of tea you're drinking!
With regards to cinnamon, the USDA has actually found (and Dr. Pratt mentions this in "Superfoods RX") that 1/2 teaspoon a day actually helped to lower blood sugar and "bad" cholesterol level in people with T2 diabetes. It aids digestion, can prevent ulcers, etc.....all good reasons to enjoy some cinnamon, but not really for the reasons you've found. I don't go out of my way to eat cinnamon every single day, but I like it and so have some in one way or another quite frequently.
I personally think the "hibernation theory" is silly - you might ease stress drinking this concoction, but that's no different than drinking ANY warm drink - milk, tea, cocoa. There is no "fat burning" metabolism - just a metabolism, and honey isn't some miracle metabolic booster. As far as "fueling the liver"...well, anything we eat or drink fuels our liver!