We put a sunroom on a north facing wall, was the only option given the orientation of the house. I was very worried about the lack of sun as other posters have said. However with the builder putting in the most insulaton he could ( don't know what values, sorry ) and with a tiled roof & 2 veluxes, facing west & east, we get an amazing amount of morning & evening sun. The room has also added to the heat of the rooms it adjoins, as the room leading to it had been a very cold one but is now much warmer. Actual sun per se is not the necessary thing, it's overall insulation & the heating system you're connected to that matters. A south facing sunroom might have more sun but would, without proper ventilation, become unbearably hot at times. Our sunroom is connected to existing kerosene system with one regular and one fan assisted radiatior. I also installed ( belt & braces approach) electric undertile heating mats which allows you to heat that room without having to use the rest of the heating system if you want.
The only thing I'd wonder about is that adding a sunroom because it's cheaper than a converntional room, just for the sake of the extra room might not be the best option long term unless you plan to use it for it's main purpose - sunroom, relaxation. If it's a playroom now, then a sunroom would do fine. But later on you can't really use a sunroom as, say, a bedroom if you had to. So I'd give long consideration to the converntional build too. The sunroom might have less walls but the cost of the extra glass & structural work might not make a huge difference in the end. Check both options.