I live here in Norway. You'll be fine in Oslo, it doesn't get that cold in February. Where I live, we have temperatures that can drop to the minus thirties, but only for a few weeks in January and this is mostly at night. I live in the mountains in one of the coldest places here.
A little tip - take decent water proof shoes/ boots. Oslo might have snow, but it's a busy city, the snow will be wet and slushy and often in a big pile where you need to cross the road. The snow ploughs drive it, but you get mounds at the side of the road.
Layers are your friend, it can be cold out. Hat, buff, gloves are a necessity, but you will need to take them on and off if you going in and out of shops etc as everywhere inside is really warm.
Jeans can be actually be very cold, so if you're going to wear them, put an underlays on as well. You really won't need to be walking around in ski gear in Oslo in February though!
Honestly, some good quality jumpers, a few merino vests (they actually might be cheaper to buy here from Cubus) and some cord trousers would be perfect with a coat. Good water proof boots are a must though!
The fjord might be still frozen in February depending on the winter we have, so you might be able to do an an ice bath followed by a sauna.
Bring a good amount of spending money, it's expensive here at the moment, even the cheaper restaurants like Egons will cost you about 1500kr for a dinner for two and maybe two drinks. Egons do however do a pizza buffet for about 175kr an adult.
Feel free to PM me, I've lived here a long time.