There is no indication when Nokia Music will be made available to iOS or Android. But we have some leaked training material along with images of the Nokia Music web app for other platforms. The Windows version of Nokia Music will be a native app and will support Windows 8/8.1 and Windows RT which means it will not be a Nokia exclusive.
Nokia Music coming to iOS and Android
1. Leaked training material
2. Screenshots of the Nokia Music web app
source: CTechcn.com (translated)