The main aim of this study was to determine consumer preferences by school-aged children and selected quality indicators of new, highly nutritive grain bars designed as a snack during school break. Consumer acceptance was evaluated by the scaling method using a five-point mimic hedonic scale. Triacylglycerols (TAG) and fatty acids (FA) composition was assayed in fats extracted from the designed bars (fresh and stored) by gas chromatography. Contents of oxidation and hydrolysis products were determined using peroxide value (PV), anisidine value (AnV), and acidic value (AV). The antioxidant activity of the ethanolic extract from bars was measured by scavenging 1,1-diphenyl-2-picrylhydrazyl (DPPH) radicals and Folin-Ciocalteau methods. The overall liking of bars was high (4.05 pts on average in the 5-point scale). The majority of children (71%) scored the designed bars as tasty and very tasty. The designed products contained 22.3% of fat with about 44 g/100 g FA of valuable fatty acids, e.g., short-chain saturated fatty acids (SCSFA), monounsaturated fatty acids (MUFA) and odd and branched chain fatty acids (OBCFA), recommended for young organisms. The content of CN52, CN54, CN50 and CN46 triacylglycerols (TAGs) (about 49 g/100 g TAG) was due to both milk and cocoa fat. Storage of bars did not influence their content of oxidation and hydrolysis products, resulting from a substantial content of total phenolics (TPC) (53.64 mg GAE/100 mL of extract) and DPPH scavenging activity at the level of 24%. The designed bars may be an interesting confectionery product for children and an alternative to snacks currently available in school shops.