The road up to Tricouni is called the High Falls Creek Road (branch 200 off the Squamish Main Line). I drove up it in April to where we hit snow at about 2,500 ft. The road was in good shape but its a bit steep and in the middle there's pretty crazy exposure. I drove up and down in 4wd low in my Pathfinder. Once you turn the corner visible from below the road mellows out and is less freaky. Way back in 1993 I had to walk all the way up this road as I was driving a Subie. We climbed a peak just south of Tricouni. It was quite a memorable trip. Was in the Spring.
Bottom line in a 2wd car you MIGHT make it up the road but your nerves might be a bit raw...