Hola!
You'll have about 9 to 10 hours of daylight, and a temperature probably between 0 and -5 degrees centrigrades (though this is an unusually cold winter). If you're lucky it is cold and sunny!
No sugestion about vegetarian dining I'm afraid. In any case, it is a foreign invention, so you'll not find unique Norwegian vegetarian tradition. Oslo is a truly multinational city, so you will find absolutely any kind of food you want. However, eating out is very expensive, and we locals very rarely do.