It's going to depend greatly on what you're baking.
Sugar serves several different purposes beyond just providing sweetness. Besides sweetness:
tenderness by interrupting and minimizing gluten formation. Sugar promotes spread in cookies
Retain moisture and extend keeping quality (in baking sugar is actually considered a "liquid" ingredient due to its hygroscopic qualities - the ability to pull moisture from it's surrounding atmosphere).
Promotes browning and caramelizing
Assists in aeration and leavening (as in creaming butter and sugar to aerate the dough)
stabilizes egg whites
Provides food for yeast growth and fermentation
In some instances you might be able to use a syrup (honey, corn syrup, molasses, etc.) but not in all cases. For instance the granular nature of sugar is necessary for aeration of cookies and cakes because the jagged edges create air pockets as they pass through the fat.
Syrups primarily serve the purposes of sweetening, browning, and moistening. Honey could be used in muffins that are being made using the muffin method (aka two-bowl method) because this method would use a liquid fat (melted butter/oil) but not in the creaming method (producing a more cakelike structure from the creaming process). When using syrups you have to account for the addtional moisture that they provide.
From: "How Baking Works" (Paula Figoni)
"The National Honey Board recommneds the substitution for using honey in place of granulated sugar. This accounts for both the amount of water in honey and for its intense sweetness: use 1 pound honey in place of 1 pound granulated sugar; reduce water (or other liquid) in the formula (recipe) by 2.5-3 ounces."
Overall, when making substitutions of ingredients that are critical to the structural and eating qualities you probably will not be able to replicate the same results with the substitution. In the end, it will often be a case of "what is the next best thing" and realizing there will be quality differences in the finished product.
I have always wondered how in anglosaxon speaking countries, people think that "mint" is always the same as "mint", just because it has the same name. In fact, spearmint tastes as different from peppermint as thymian from oregano. Almost all cooking recipes I know of are meant for spearmint, except for some sweet applications. All mint tea I have encountered is made from peppermint, not from spearmint. So while you can use dried spearmint instead of fresh mint, using mint tea is a bad idea, unless yours happens to be an exception made from spearmint.
You could try finding out if a herbs seller has dried spearmint, but you must remember that it has less aroma than fresh spearmint. Also, dried mint does approximate the aroma of the fresh one when used as a herb, but when used in big quantities (you mention 1 cup) as a vegetable on its own right, the substitution is much more problematic, because juiciness and texture are much more different.
I don't know about the situation where you live, but spearmint isn't used much in Western countries, except maybe England, so it is seldom available at supermarkets and costs a lot there. A better source are Turkish grocery shops, where it is as common as parsley, and the price is comparable. If there are Turkish shops nearby, it is definitely worth trying to find it there.
For a longer term solution, it might be a good idea to grow your own spearmint in pots. The plant is quite unassuming and easy to care for, and a kitchen which smells of fragrant herbs is nicer than one which smells of frying grease or cleaning products.
Best Answer
There are absolutely no substitutes, neither cheap nor expensive.
First, the cooling effect is due to a very rare coincidence. It so happens that menthol is chemically capable of activating one of the temperature receptors in human skin (also present in the lining of the mouth). There are no other substances which do the same thing, at least not ones known in cooking (and if there happens to be some exotic option, it will certainly be more expensive to get hold of).
Also, even if you could mimic the cooling effect of menthol, you would never find a substitute which also smells of menthol, so people will readily notice the difference.
That being said, I am surprised that you find menthol very expensive. I found that I can get natural mint essential oil (which is about 50% menthol) for 8 Euros for a 40 ml bottle. This should be enough to aromatize about 400 kg of candy. And we are talking about expensive, naturally created stuff sold to hobbyists in a country with high standard of living. It could be possible to find synthetic menthol at cheaper rates somewhere, most likely at a pharmacy. Of course, it could turn out that there is no good supply where you live and the few people who sell it demand too much, but this would surprise me if it is a commonly used ingredient in your culinary tradition.
If you find that pure menthol is for some reason too expensive for your pocket, e.g. because the smallest batch you can buy is more than you will use up in a lifetime, you could just look at products meant for cooks which are basically diluted menthol. This includes mint extracts, mint syrups, mint essential oil, and a lot of other options, varying by region.