Oleander In Oklahoma . When you start winterizing oleander plants in this zone you need to cut back the shrub in autumn by half. 5 to 10 degrees celsius. Pelargonium Nerium (Oleander) from pelargoniumpl.blogspot.com It contains chemicals called toxic cardiac glycosides, which can lead to death when consumed. Probably not a good time to plant oleander. It’s versatile and makes a good border, hedge, or screen,.