[underscore]

The usual stuff applies with mountain passes, take it easy and only do it with good snow tires. A lot of the time it's fine with meh tires but the weather up there changes fast and what was fine for your drive out might not be good enough for the drive home. I've driven down on mostly clear pavement and driven back the next day doing about 40km/h on compact snow and ice, passing flipped and stuck vehicles all over the place. The only time I took the Hope Princeton during the "winter" was because it was right at the start of the season and I had crap tires so I was trying to avoid the summits. I went all the way down to Penticton and it was 3hrs longer to Kelowna. I wouldn't take it in the winter if it could be avoided, there's a lot more places from Hope to Princeton where if you go off the road it's gonna be sketchy. If you go north from Princeton to the connector it's a little less sketchy (aside from the lakes) but there's next to no traffic so if you need help it might be a while. That may be the influence of all the horror stories I heard from my grandfather who was a trucker and drove it a lot though. I would think the Coq/Connector is a higher priority for plows and stuff too.

As 320icar said fog can come out of nowhere on the Connector, and clear up just as fast. Going full speed and suddenly not being able to see the road or the shoulders has a pretty high pucker factor when there's not enough snow for the big banks yet. When the snow banks are built up it's great to drive at night in a car because you're low enough that oncoming lights can't hit you and you can leave your highbeams on all the time. The Pennask Summit (1,728m) is also much higher than the Coquihalla Summit (1,244m) but everyone seems to forget about it and get caught out up there, so check the highway cams for both before you go.

tl;dr - take the Coq/Connector and don't drive like an idiot and you'll be fine. Bring snacks, warm weather gear, etc in case the road gets shut down for any reason and you're stuck.