I'm visiting Norway and Sweden in October and am thinking of driving from Kirkenes to Stockholm (or Oslo). What are the road conditions like at that time of the year? Coming from Australia I have never driven in snow / ice conditions and am a little nervous about this option but think I will be able to explore better this way than on a bus.
In October the only useable word for the road conditions is "constantly changing" and you should be prepared for (nearly) everything. You may start the day exploring +2 degrees Celcius, the most beautiful autumn weather imaginable and a nice road with one wide lane in each direction. Later this day you may explore -15 degrees Celsiums, a harsh storm including a little snow giving you 20 metres/65 feet of sight, a VERY slippery narrow hair-pinned road being maximum 3.5 meter/11.5 feet wide total for both lanes climbing up and down the mountains, meaning that your real speed is 10-15 kilometers/6-10 miles pr hour and that you may return that road backwards for a couple of kilometers if you meet a bus or a large commercial car. Suddenly you may end your day a bit "to early" by exploring a a road covered by 3/4 meter (2.5 feet) of snow, presently closed, illegal to drive and "possible opened later today, more possible opened tomorrow and in worst case opened the next week".
You should in the north also be prepared for a sunrise at 9-10 am and a sunset at 2-3 pm. Further you should remember that the the distance is approximately 2500 kilometers at roads allowing you a REAL speed of 40-50 kilometers/hour in average in October. The speed limits are further enforced strictly from the view that "maximum allowed speed means MAXIMUM allowed speed, 0.2-5 kilometers/hour more = a fine equal to 150 USD, 20.2-30 kilometers/hour more = a fine of minimum 1500 USD and maximum 6000 USD (depending on your salary), a driver's license (and passport) withdrawn on spot and returned Australia - and jail detention if the police and court consider your driving as "dangerous". about 4 years ago
Recommendation #1: If your intention is to EXPLORE the northern part of Norway, you should neighter use bus (and there are no buses covering all the distance between mid-October and late March/early April) nor car. You should use the coastal steamer leaving Kirkenes nearly every day (day 1) in the morning and arriving Bergen in the early afternoon day 6. From Bergen to Oslo you'll Sunday-Friday night have the choice between a nice night train with single bed compartments priced at 200-225 USD if maximum comfort is preferred and a high-quality and quite comfortable night bus at about 100 USD if cheapest possible price is preferred.
If budget and price aren't real subjects, just choose a day and book the coastal steamer a couple of weeks ahead and you'll get a ticket and a bed in October. If budget and prices are real subjects, you should preferably try to leave a day a "mid generation ship" (three of twelve, constructed 1980-1984) is scheduled as the accommodation is clearly cheapest on these ships (starting at about 1500 USD for ticket, inside double bunk bed cabin single use and full board). Remember that it is along the coast you will explore the small towns and the people, NOT along the main road (unless driving "down" to the towns from the main road - 100 kilometers/60 miles here and 200 kilometers/120 miles there..) about 4 years ago
Recommendation #2: If your intention is to rent a car in Kirkenes and leave it in Oslo/Stockholm, expect that will cost you a bit of money, WAY more than using the costal steamer. Car rental is expensive - as in EXPENSIVE - in this area! In October you should roughtly calculate as total cost - all taxes and fees inclusive - for a small car:
a) Not less than 10 days rental @minimum 100 USD/day - 1000 USD, compulsory insurance included.
b) 5000 kilometers/3000 miles@no less than 0.25 USD/km - 1250 USD
c) Petrol for 5000 kilometres/3000 miles@about (due to taxes and transport) 2 USD/litre or 9 USD/gallon.
d) Fee for the person returning the car to Kirkenes - if ordinary salary is paid minimum 4 days@minimum 150 USD/day included company's overhead cost, and very possibly 250-300 USD/day. (Salary can be discussed if using the car early in October, so that in may be returned by a person willing to do the work for free/nearly for free in the Scandiavian "autumn school holiday".)
e) Food and accomodation for the person mentioned in d) - by law about 200 USD/night for accomodation and about 70 USD/day for food, subjected that the person has stayed in hotels. (Also to be paid to a person returning the car for free).
f) Very possible a one-way airplane ticket Kirkenes-Oslo/Stockholm for the person mentioned in d).
In addition add 4-5 night's stay at absolutely minimum 150 USD/night and food needed during the travel (and remember that even a hot-dog and a bottle/box of Cola in this area means 10 USD!) about 4 years ago