Well, it won't be so great, but it won't be as bad as, say, January/February...
We went to Sweden (Stockholm) in February, and had a blast despite the snow on the ground and the ice in the river. Yes, it was cold but that's part of the place, you know? Also, during the few daylight hours, the weather was fabulously clear and sunny - so while it was light, it was really pleasant. By March, the days'll be getting a little longer, though it'll still be cold and there'll probably still be some snow around, I'm guessing. Travel guide books (we like Lonely Planet's "Scandinavia") would give you a rough estimate of the kind of weather you could expect.
Weather aside, I love traveling in the off season, and early spring will be great - just check and see if your dates coincide with Easter - there will probably be a lot more people traveling during that week, since the kids will be off school - but with any luck all the northerners will opt for someplace like Spain and you won't have to contend with great tourist hordes.
Still, there should be plenty of people in the hostels to meet and hang out with. As I mentioned, we were in Stockholm in February and stayed in a great hostel there - the "Af Chapman" - great location, breakfast included, but take your own sleep sheet if you can, their rental rates seemed steep. The hostel was by no means full at that time, but there were probably 10 other people staying on the ship part of the hostel, and probably another 40 or so in the building on shore, which is where the common and breakfast rooms are. It seemed like they put most of the single, young people on the ship, and the families in the building, but we stayed on the ship with our 4 little kids in a 6 bed dorm - you can state your preference, though they can't guarantee you'll get it.
Another advantage traveling that time of year, is that you're more likely to meet local travelers - people from other parts of the same country, or from neighbouring ones - which can give you someone to meet up with later on in your trip - maybe even a free place to sleep, if you luck out.
There are plenty more good reasons to travel off-season, but I'll throw out just one more for now - in March/April, the winter "cultural" seasons are still in full swing, so if you are interested in going to concerts, ballets, plays, operas etc, you'll have plenty to choose from. Often the seasons taper off by May and summer travelers miss out on a very interesting experience and some really terrific performances.
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