Low-dimensional materials, such as ultrathin films, nanoislands, and wires, are actively being studied due to their interesting magnetic properties and possible technological applications for example in high density data storage. Results of density functional theory calculations within the generalized gradient approximation of an Fe nanoisland on a W(110) surface are presented here with particular focus on the effect of hydrogen adsorption on magnetic properties. The adsorption is found to strongly decrease the magnetic moment of the Fe atoms the H atoms are bound to, down to less than a half in some cases as compared with the clean Fe island. This is an important consideration since hydrogen can relatively easily be introduced and removed from the system, thus providing a way of tuning magnetic properties, and it can also be unintentionally present even under ultrahigh vacuum conditions, especially at low temperature.