One of the most advanced approaches to querying data in the presence of ontologies is to make use of relational database systems, rewriting the original query and the ontology into a new query that is formulated in SQL or, equivalently, in first-order logic (FO). For ontologies written in many standard description logics (DLs), however, such FO-rewritings are not guaranteed to exist. We study FO-rewritings and their existence for a basic class of queries and for ontologies formulated in Horn DLs such as Horn-SHI and EL. Our results include characterizations of the existence of FO-rewritings, tight complexity bounds for deciding whether an FO-rewriting exists (ExpTime and PSpace), and tight bounds on the (worst-case) size of FO-rewritings, when presented as a union of conjunctive queries.