The increase in life expectancy led to a significant rise in the prevalence of age-related neurological diseases, such as cognitive impairment, dementia, and Alzheimer’s disease. Although genetics certainly play a role, nutrition emerged as a key factor in maintaining optimal cognitive function among older adults. Therefore, the study aimed to investigate whether specific categories and subcategories of dietary fats, based on carbon-chain length, are associated with cognitive status in a cohort of 883 Italian participants over the age of 50. Methods: The intake of total, single class of dietary fat, such as saturated fatty acids (SFA), monounsaturated fatty acid (MUFA), and polyunsaturated fatty acid (PUFA), and also single fatty acids grouped according to carbon-chain length, were evaluated by food frequency questionnaires (FFQs). Cognitive health was assessed using the short portable mental status questionnaire (SPMSQ). Results: After adjustment for potential confounding factors subjects with a moderate consumption of both short-chain SFA (for Q2 vs. Q1, OR = 0.23, 95% CI: 0.08, 0.66) and middle-chain SFA specifically lauric acid (C12:0) intake (for Q2 vs. Q1, OR = 0.27, 95% CI: 0.09, 0.77) were less likely to suffer from cognitive impairment. Among single MUFAs, erucic acid (C22:1) intake resulted in an inverse association, in a linear way, with cognitive impairment (for Q4 vs. Q1, OR = 0.04, 95% CI: 0.00, 0.39). Conversely, moderate intake of linoleic acid (C18:2) was associated with cognitive impairment (Q3 vs. Q1, OR = 4.59, 95% CI: 1.51, 13.94). Regarding other PUFAs, individuals consuming moderate intake alpha linolenic acid (C18:3) were less likely to have cognitive impairment (for Q3 vs. Q1, OR = 0.19, 95% CI: 0.06, 0.64). Conclusions: Total SFA intake appeared to be inversely associated with cognitive impairment. Regarding specific subtypes of fatty acids, the results mostly referred to short- and middle-chain SFA. Further studies are needed to validate the results of the present study.