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.
Programs: AA EXP 1.7 M, Hilton Gold, Hertz 5*, AARP Sophomore, 14-time Croix de Candlestick
Not to be missed: Climb to the top of the new (2008) Opera House! You can easily reach the Opera House from the main train station via a connecting footbridge. here are photos I took last September, including some taken from the roof:
There are plenty of things to do, but you haven't told us anything about what you like! And what kind of music sounds good to you?
The one thing you should make absolutely sure you don't miss is the viking ship museum. Also, your hotel is close to the national gallery which has free entrance, if you are interested in art.
+1 to the National Gallery. The highlight is one of the originals of Edvard Munch's "The Scream" - the work surprised me both by its size (larger than I had imagined) and for the intensity of the coloring. The Gallery is no one-trick pony - many of the other works of art are well worth looking at.
Agra restaurant on the pier is really really good for indian.. which means you'll find good vegetarian. i would skip the viking museum (too small) and see the vigeland sculpture park if its not too cold
Depending on how much you like museums I would consider a trip to:
1 either the museum peninsula (Bygdøy) with the Viking Museum, Folk Museum (with lots of traditional Norwegian buildings, including a stave church in one parklike area), Kon-Tiki Museum (Thor Heyerdahls fleet and boat), Fram (Amundsens South Pole expedition ship) and the Maritime Museum.
2 Otherwise the Tøyen Museums, which has the Munch Museum as well as our Natural History Museum including the Ida exhibit.
The bondeheimen hotel should have a decent restaurant for more tradition Norwegian food and right across the street (or was it one block down) is New Orleans restaurant which is in the upper price range but very good. They like most restaurants have some vegetarian options.
I would also add a vote for the Vigeland Sculpture park, as well as a walk up and down Karl Johan street, that gives you one of the older Churches in Oslo, the central station, the Parliament as well as the Royal Castle. Both that and Aker Brygge is kind of expensive but it wont be so touristy now in februar.
Vegeta Vertshus, Munkedamsveien 3B, is a vegetarian buffet not far from the National Theater. It's also one of the more reasonable places to eat in an expensive town. Not refined but definitely filling. The cafeteria at Bondeheimen will have some salads, as well as down-country Norwegian dishes.
Depending on your dates and the kind of music you like, By:larm, Feb 18-20 might be up your alley.
In recent years the museums have been free on Sundays outside of the main tourist season.
Bundle up and walk around -- there's lots to see. Vigelund Park is quite moving (I expected kitsch). The bas reliefs on the exterior walls of the courtyard of the Town Hall are quite interesting, depicting Norse mythology. The harbor is worth seeing, both from the Aker Brygge side and from the fortress hill.
Be sure your boots have a good tread, or invest in some pyggs (spikes to slip over your footwear. Snow removal is efficient but the sidewalks can be very icy and the few cinders sprinkled around don't do much.