Can I replace the sugar in ice cream with (very smooth) applesauce. I do not enjoy my desserts to be super sweet and I always have tons of homemade applesauce sitting in the fridge. How much would this affect the texture?
Ice cream needs a certain ratio of solids to liquids to work. Sugar is an important solid in ice cream. As applesauce is mostly water, you can't replace all, or even most of the sugar.
The amount of carbohydrates in applesauce will vary depending on how much you cooked it down, but based on a few nutrition data results for the commercial variety, it seems that 40% carbohydrates is a reasonable assumption. So you want to remove some sugar and milk and add the applesauce and some butter (to compensate the missing fat). Calculating with 8% non-fat solids and 4% fat in the milk, and 83/17 fat/water ratio in the butter, we get following substitution: for each 10 g of sugar you remove, you also have to remove 20 g of milk, and add 29 g of applesauce and 1 g of butter. You probably need a recipe with emulsifiers to get the butter into it.
Most ice cream recipes will have much more cream than milk, and so not much milk available to remove. You'll have to recalculate to get the amount of butter needed when you are replacing cream. But the more dairy you remove, the more you are changing the flavor. While the texture is likely to keep up well (the pectin from the applesauce will probably do a good job to reduce ice crystals), the taste will move in direction sorbet. Depending on your expectations, this might be OK for you, or it might be a problem.
As for reducing sweetness, I am not sure this will happen. At very cold temperatures, sugar loses much of its perceived sweetness. Fructose loses some, but not all. And apples are very high in fructose. So, even though not all carbohydrates in applesauce are sugars, you might end up with a quite sweet ice cream. On the other hand, if you used sour-ish apples, the perceived sweetness will be low. There is no way to tell but try it out.