Stormwater is a source of pollutants in urban areas and should be treated to prevent negative environmental effects. A newer technique uses floating rafts with plants, called floating treatment wetlands (FTWs), which are placed in the polluted water. Few earlier studies have examined heavy metal removal by FTWs, and none has examined stormwater in cold climates. This study therefore aimed to determine whether plants growing in FTWs could accumulate heavy metals from stormwater ponds in a cold climate. This study examined the abilities of three native wetland species (i.e., Carex riparia, C. pseudocyperus, and Phalaris arundinacea) to accumulate Cd, Cu, Pb, and Zn. The plants were planted on FTWs, which were placed in two stormwater ponds in Stockholm, Sweden, for 12 weeks. Phalaris arundinacea accumulated more Cd, Cu, and Zn than did the Carex species, and C. pseudocyperus accumulated less Pb than did the other species during the experimental period. In most cases, the roots had higher metal concentrations than did the shoots. Carex pseudocyperus had smaller differences between shoot and root metal contents, whereas P. arundinacea had higher Cd and Cu contents and lower Zn contents in its roots than in its shoots. The metal content in the plants increased with higher biomass. The plants that grew in the stormwater pond with a higher Zn concentration had a higher Zn tissue concentration and total Zn content per plant after treatment. This study shows that wetland plants growing on FTWs can accumulate metals from stormwater ponds in a cold climate. Phalaris arundinacea appears to be a good candidate for metal removal use in FTWs. Furthermore, high plant biomass positively affects the metal uptake, meaning that good growing conditions could be essential for metal removal.