We did this in 2015 and had an awesome time. We went with Transun and stayed in Karesuvanto/Karesuando. It is pretty remote round there and is about 100km from the nearest town. We did a snowmobile trek, reindeer sleigh ride and drove huskies across a frozen lake. We were also lucky enough to see the northern lights.
It was one of the best holidays we have ever had, but not cheap. We had snow suits provided but we still had to buy clothes to layer underneath, hats, gloves, snoods etc. I must have spent a 3 figure sum in Decathlon. Don't underestimate how cold it is.