The use of sucrose-alternative sweeteners in ice cream production could satisfy requirements of modern consumers focused on natural and nutritionally balanced foods. The aim of this work was to fill the gap in basic knowledge about the effects of honey, trehalose, and erythritol on the properties of artisanal ice cream. A milk-based sucrose-sweetened ice cream was produced as reference sample (REF), using then the alternative sweeteners to partially (50%) or totally (100%) substitute sucrose. With respect to REF, honey-containing ice cream mix revealed a significantly lower value of soluble solids (30.4°Bx vs. 34.5°Bx) and apparent viscosity (36.5 mPa s vs. 47.6 mPa s) and a significantly higher extrusion time (8.18 min vs. 7.04 min). The total substitution of sucrose with trehalose and erythritol led to a melting rate (2.07 and 1.56 g/min, respectively) significantly lower than REF (2.75 g/min), a very high firmness (508 and 725 N vs. 4 N), and a higher extrusion temperature (−7.1 and −5.3°C vs. −9.3°C). The results of this study represent a guideline for the successfully utilization of honey, trehalose, and erythritol in peculiar ice cream formulations (e.g. non-sweet or low-calorie products).