If you want to avoid the usual cookie-cutter tours offered by the Ice Hotel, I really suggest checking out White Trail Adventures.
Starting some weeks before our visit I was hunting around for a non Ice Hotel tour company. We were traveling with a couple that had been to the Ice Hotel several times previously, and suggested we go with a local/smaller tour guide for something different. We also wanted a private tour, not in a pack of 10 snowmobiles. I stumbled on WTA and was able to get something quickly arranged.
First, the basics: logistics were all fine. Booking was easy and quick. We were picked up on time. All the equipment worked. We found it good value for money in two ways: 1) the trip lasted most of the day, not just the booked hours on the dot like an Ice Hotel tour; 2) it was a lot cheaper than what the Ice Hotel offers. Guide was competent and professional (if not downright colourful!). Can pay by credit card - a big plus so you don't have to carry around a wad of krona.
So that's all positive, but really just the minimal bar you might expect any independent tour company. So what're the main reasons to go with this tour company versus the easy choice of an Ice Hotel arranged tour?
First, It was just so "real" and so not "the formula". We were on trails where we saw no-one else, just lots of beautiful countryside and local critters (lots of reindeer). It lasted as long as it did, to its own timetable, not an imposed one. We stopped when we wanted or when the guide thought we needed to warm up a bit.
Second, and the best reason, is that the guide was great, a real character. He's the kind of guy you'd want around if something went wrong during the tour - he would just fix it. So a big thanks to Björn, our guide. His local knowledge was great, and we stopped periodically along the way for him to explain animal tracks in the snow, local history, Sami culture, and anything else that popped into his mind. He fielded all our questions. He was passionate about living in Sweden and in the area around the Ice Hotel. He showed great respect for the world around us, stopping for awhile at one point so we didn't break up a reindeer herd making their way across our intended path.
One other reason to book independently - the Ice Hotel makes a big premium off of making a 3 minute call to a company like this to subcontract out their guest's tours. Better to spread the wealth a bit!