Surtingshue lies 2368 MASL and the starting point is Memurubu Tourist Cabin by Gjende. The mountain lies in Jotunheimen National park and the view is fantastic. There is routh is marked from Memurubu. The hike is quite demanding, it is not unusual to spend 8-9 hours on this hike. Maybe even more.
You can spend the night at Memurubu and ski from there. Should Memurubu be closed you may start from Gjendeosen and ski inn towards the ice to Memurubu and reach the top within a day. This requires you to have good stamina and know your way around skies. The ice on the mountain water rarely freeze before January, and becomes unstable again relatively early in the spring. It might benefit you to ask some locals about the ice conditions here.