Losing Power on Hills, 2012 Lancer
 

I have a 2012 Lancer, with a little under 100k on it, I live in a part of Canada with rough winter's and steep hills, I have found that the car has little to no traction even with brand new winter tires. I also find that when going up steep grades, that I cannot keep my rpm at a steady rate, it will shoot to high rpm, then back to low, and keep doing this until I reach the top of the grade. I can be going 80km/hr starting the hill, and by the time i'm half way up, I will be going 20-30km/hr, with little amounts of snow on the hill. Any explanation to why this is happening?