I've been up this canyon many times, especially as a youth, and it is one of my favorite places in the whole world. Home to some of the most famous rock climbing spots in Utah (if not the world), it is a climbers paradise. Just drive on up and see the conglomerate stone, and then tell me that doesn't look like the Maker Himself didn't create that with climbers in mind.
This is at the mouth of the canyon, where the paved road ends, so even in the winter, due to its position, it should always be accessible (unless the snow is REALLY deep). I did consider leaving the GeoTour cache at this location, but then some folks might not go further up the road a bit...and if you have gone up the road to where that cache is, you KNOW that would be a real shame. So, in the unlikely event that you really DO want to go up the canyon for that cache or others, but the weather is having none of it, here is your consolation prize. Have fun, and feel free to share some photos / words about your adventures!