If you are a dog lover this trip is a must - if not, don't go! You will spend a lot of time with the dogs and will handle them and care for them. In the end you will probably pretty much smell of them!
In terms of fitness and strength: you definitely don't need to be a super-athlete or stong, but a reasonable level of fitness will make the experience more enjoyable because you will be active most of the day.
Be prepared for basic, shared, accommodation. The cabins are nice and warm but toilet trips require a visit to an outbuilding and if you want to wash you'll be doing it outside. The only exception is the night spent in the Sami town, Ovré Soppero, where you can have the amazing experience of having a good wash inside the sauna!
This is very much also a group experience and you will need to pitch in and help with the cooking, washing up, feeding dogs, getting wood and other chores that need to be performed. Our group was great and I found the group experience very rewarding.
Exodus provides excellent equipment but I would suggest you take thermal underwear (top and bottom), some form of mid-layer and a fleece tops and some comfortable trousers to wear under the overalls. Definitely take some polartec gloves to wear inside the mittens provided and to use when doing things that are not so easily done with mittens - such as harnessing the dogs. I also took 3 pairs of thick winter socks with 3 pairs of liner socks. Don't skimp on the quality of your socks. Your feet are likely to be the coldest part of you and most easily get damp. I come from a warm climate and I was very glad that I had a good down jacket, a balaclava and a thermal sleeping bad inner. I didn't need the running shoes that I took along and found the boots provided sufficient for the whole trip. You should definitely take a good head torch with spare batteries.
If you enjoy a drink in the evening then I would definitely suggest taking some vodka, or equivalent, along. The evenings in the cabins were great fun and some shared drinks definitely added to the experience.
Don't be put off by the cold. I travelled from temperatures 40 to 50 degrees warmer than we had during our trip and I was fine! If you have warm clothing you will be fine.
Take a good digital camera with spare batteries and space to take lots of pictures! You will have lots of great picture moments.
Don't be surprised if you start thinking about going back!!
Lastly, I travelled all the way from Cape Town and I was really impressed with Exodus. Every little detail was taken care of and the whole experience was slick from the moment I decided to book right up to my return.