If you wish to visit the Arctic but not organize and expedition yourself, you could consider a visit to Iqualuit, Nunavut. Iqualuit is usually described as being "in the Arctic" though it is not technically inside the Arctic Circle. Lots of Arctic winter activities are available, including snowmobiling, dogsledding, viewing the unique wildlife of the region, igloo building.
You can find similar activities in northern Canadian towns like Dawson, Yellowknife or Inuvik (which is technically inside the Arctic circle).
(Not affiliated with the linked company nor do I reccomend them - they are simply an example)