One definition of 'cognition' is 'the mental action or process of acquiring knowledge and understanding through thought, experience, and the senses'. Whether an animal has high or low cognitive abilities, they will be able to learn and solve 'puzzles' to some extent, although it is important to understand the limits of each species in order to provide species-appropriate activities. Novel experiences and activities also stimulate cognitive processes as an animal explores and tries to understand new things, these do not have to be complex but should be something that they have not experienced in the same way before. Altering previously used activities or providing brand new ones is a good way to ensure the cognitive aspect of enrichment persists.
Focus on encouraging hunting and feeding behaviours. Think about where they would find their prey, how they would stalk, chase and catch their prey and any species-specific hunting behaviours or adaptations. Food items including fur and feathers will encourage natural feeding (and sometimes play) behaviours and increases the time taken to consume food.