Will the roads be slippery in december end?

Yes. 100% expect winter driving conditions. There is a pass between Park City and Salt Lake, typically weather between Salt Lake and Twin Falls (even though there technically isn't a mountain pass there is a major weather corridor through there), and then there is a mountain pass between Baker City and Pendleton.
I am from Ketchum, Idaho and used to live in Portland so I've done that drive many, many times. When I moved from Portland back to Idaho in January 2002 I had to outrun a winter storm all the way from Portland to Boise, it was crazy.
During the 11 years I was back in ID, my brother lived in Park City for several years so I've also done the Twin Falls to Park City drive more often than I can count. We used to go to PC every Thanksgiving and the roads were almost always winter driving even in November.
Honestly, it's so inexpensive to fly I'm not sure why you'd drive unless you like winter driving.