We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL's COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt (LICS 2017), who showed that query evaluation for this logic is fixed-parameter tractable on classes of databases of bounded degree. In the present paper, we first show that the fixed-parameter tractability of FOC(P) cannot even be generalised to very simple classes of databases of unbounded degree, such as unranked trees or strings with a linear order relation. Then we identify a fragment FOC_1(P) of FOC(P) which is still sufficiently strong to express standard applications of SQL's COUNT operator. Our main result shows that query evaluation for FOC_1(P) is fixed-parameter tractable on nowhere-dense classes of databases.